Monday

April 21, 2014

April 21, 2014

Number of results: 88

**Trigo!**

Ok, i did this maths trigo question, that says sinx-cos=2/3. I squared it on both sides to get sin2x=5/9 and did the sum. In the end i got two solutions, 16.9 and 73.1. However, when i substituted the answers back into the equation, only one of the 2 answers was correct! The ...
*Saturday, September 19, 2009 at 2:21am by help!*

**Math**

A sketch is available at the following link: http://i263.photobucket.com/albums/ii157/mathmate/Trigo.jpg
*Wednesday, July 15, 2009 at 12:57pm by MathMate*

**trigo**

Tony is correct.... :)
*Saturday, July 31, 2010 at 11:02pm by Henni*

**trigo**

height=793.561
*Tuesday, August 3, 2010 at 7:03am by Anonymous*

**Trigo!**

sorry, i found my mistake already.
*Saturday, September 19, 2009 at 8:35am by help!*

**trigo**

Grade = h / L 0.1 = 10 /L L = 100 METERS
*Sunday, August 1, 2010 at 9:05am by Henry*

**trigo**

Grade = h / L 0.1 = 10 / L L = 100 Meters
*Saturday, July 31, 2010 at 10:54pm by Henry*

**trigo**

bobo nung unang sumagot ,
*Saturday, July 31, 2010 at 11:02pm by paul*

**trigo**

Check your 4:12am post for solution.
*Tuesday, July 12, 2011 at 4:23am by Henry*

**trigo**

tan A = OPPOSITE/ADJACENT = 1250/1760
*Sunday, August 1, 2010 at 1:10am by Damon*

**trigo**

oops A is 50° (90° - angle of depression)
*Tuesday, October 18, 2011 at 10:58am by Steve*

**Trigo**

let the time be t hours solve 18t + 22t = 250 (How is this trigonometry ? )
*Thursday, June 28, 2012 at 7:58am by Reiny*

**trigo**

what is the basic way to study this topic??i mean trigonometery......it's kinda difficult
*Friday, November 20, 2009 at 8:04am by Michael*

**trigo**

I cannot make sense out of your description. Where doe Gold Street come from?
*Monday, August 2, 2010 at 6:53am by Reiny*

**TRIGO**

Let z=tan^2(x), z>0 F(z)=9z+4/z, F'(z)=9-4/z^2, F'(z)=0 if z=2/3 minF(z)=F(2/3)=12 (corresponding value of x exists)
*Friday, June 3, 2011 at 5:25am by Mgraph*

**trigo**

1. (1-sin²B)/(sin²Bcos²B)= csc²B-sec²B --that's really the given. please help.
*Saturday, December 13, 2008 at 6:52pm by Anonymous*

**TRIGO**

Find the minimum value of 9Tan^2x + 4Cot^2x.
*Friday, June 3, 2011 at 5:25am by anandi*

**trigo**

4.2x2-1.2x6-0.018x5 divided by -6x4 =? 18y3-5y12-7y11 divided by 3/2y =?
*Monday, July 26, 2010 at 6:12am by weakin*

**trigo**

the L and C State building is 1,250 m tall. What is the angle of elevation of the top from a point on the ground 1,760 m from the base of the building?
*Saturday, July 31, 2010 at 11:22pm by trigofunctions*

**trigo**

calculate the amount of each annuity of the last deposit.A deposit of $450 at the end of each month period of 5 years at 6.5% compounded semi annually.
*Tuesday, June 9, 2009 at 4:59pm by dora*

**trigo**

The L and C State Building is 1,250 m tall. What is the angle od elevation of the top from a point on the ground 1,760 m from the base of the building?
*Sunday, August 1, 2010 at 1:10am by trigofunctions*

**trigo**

Because of the wind, a boat sails 4,728 meters in the direction S 47deg29mins W. How far south it goes? How far west has it gone?
*Tuesday, August 3, 2010 at 6:59am by trigofunctions*

**trigo**

calculate the amount of each annuity of the last deposit.A deposit of $450 at the end of each month period of 5 years at 6.5% compounded semi annually.If you dont have my email how i am going to recerive the answer?
*Tuesday, June 9, 2009 at 5:01pm by dora*

**trigo**

from the top of a cliff 126m high, the angle of depression of a boat is 20.7deg. how far is the boat from the foot of the cliff?
*Saturday, July 31, 2010 at 11:02pm by trigofunctions*

**trigo**

And no one is going to answer that question. After you do the work, one of the teachers will be happy to make suggestions or corrections. We do not do your work for you.
*Tuesday, August 3, 2010 at 7:03am by GuruBlue*

**maths trigo**

prove that sin(n+1)A-sin(n-1)A/cos(n+1)A+2cos(nA)+cos(n-1)A=tanA/2
*Sunday, September 30, 2012 at 9:25am by ankita*

**trigo**

-1.2X^6 - 0.018X^5 + 4.2X^2. 6X^2(-0.2X^4 -0.003X^3 +0.7)
*Monday, July 26, 2010 at 6:12am by Henry*

**trigo**

The product of radius and angle turned through is the same for both wheels. The smaller wheel turns faster. 24*26 = 16*theta theta = 1.5*26 = 39 radians
*Friday, December 28, 2012 at 12:09am by drwls*

**trigo**

how do i verify these? 1-sin^2B 1. ----------- = csc^2B-sec^2B sin^2Bcos^B 2. cos(2a+a) = 4cos^3a-3cosa
*Saturday, December 13, 2008 at 6:52pm by anjelica318*

**trigo**

In a right tringle,/_ABC has a value of 37 degree while its opposite side is equal to 5,where angle c=90 degree find: a.) Remaining sides of the triangle b.) /_ABC using any trigonometry functions
*Tuesday, July 12, 2011 at 4:12am by William john*

**Trigo**

Two men travelling in opposite directions at the rate 18 and 22 miles per hour respectively started at the same time from the same place. In how many hours will they be 250 miles apart?
*Thursday, June 28, 2012 at 7:58am by Alice*

**trigo**

Points A and B are on the same horizontal line from the foot of a hill and the angles of depression of these points from the top of the hill are 30deg and 22deg, respectively. If the distance between A and B is 75m, what is the height of the hill?
*Tuesday, August 3, 2010 at 6:28am by trigofunctions*

**trigo**

amount = payment[(1+i)^n = 1)/i ] monthly rate = .065/12 = .005416666 amount = 450[(1.005416666^60 - 1)/.00541666 ] = 450(70.67397614) = 31803.29
*Tuesday, June 9, 2009 at 4:59pm by Reiny*

**trigo**

angle Z = 90- 27.7 = .... y/14 = tan27.7°, y = 14tan27.7° = ... 14/x = cos27.7°, x = 14/cos27.7° = ...
*Monday, February 21, 2011 at 7:18am by Reiny*

**trigo**

a bridge is 10 meters above the original ground n assumed to be level. How far from the end of the bridge, an approach starts, if the approach is to have a 10 percent grade?
*Saturday, July 31, 2010 at 10:54pm by trigofunctions*

**trigo**

a bridge is 10 meters above the original ground n assumed to be level. How far from the end of the bridge, an approach starts, if the approach is to have a 10 percent grade?
*Sunday, August 1, 2010 at 9:05am by trigofunctions*

**trigo**

Two points, A and B, are 526 meters apart on a level stretch of road leading to a hill. The angle of elevation of the hilltop from A is 26deg30mins, and the angle of elevation from B is 36deg40mins. How high is the hill?
*Tuesday, August 3, 2010 at 7:03am by trigofunctions*

**trigo**

Frankly, there is a lot of memory in Trig. Flashcards are helpful. Practice problems are helpful. I also strongly recommend Schaum's Outline Series, Trigonometry, available at most bookstores, it is really good, and inexpensive. Visit a local BarnesNoble, and take a look.
*Friday, November 20, 2009 at 8:04am by bobpursley*

**trigo**

The pilot of an airplane left A and flew 200 miles in the direction S 20deg20mins W. He then turned and flew 148 miles in the direction S 69deg40mins E. If he now heads back to A, in what direction should he fly?
*Tuesday, August 3, 2010 at 6:39am by trigofunctions*

**trigo**

from the top of 90 meters high building it is observe that the top of another building make a 40 degree angle depression. if two buildings 75 meters apart how tall is the other building?
*Tuesday, October 18, 2011 at 10:58am by jayson austria*

**trigo**

In a right tringle ,angle ABC has a value of 37 degree while its opposite side is equal to 5,where angle c=90 degree Find A.)Remaining sides of the triangle B.)Angle ABC using any trigonometry Functions
*Tuesday, July 12, 2011 at 4:23am by William john*

**trigo**

a tugboat is 36km due north of lighthouse C. Lighthouse B is directly east of lighthouse C. The lighthouses are 53km apart. Find the bearing og lighthouse B from the tugboat and the distance of lighthouse B from the tugboat.
*Monday, August 2, 2010 at 6:33am by trigofunctions*

**trigo**

I see a straightforward right-angled triangle TCB where C is 90°, CT=36 and CB = 53 using the tangent ratios angle T = 55.8° I will leave it up to you to find the angle using whatever format your course or text book uses. I would call it a bearing of 124.2°
*Monday, August 2, 2010 at 6:33am by Reiny*

**trigo **

A passenger on a ship sailing north at 5.0 mph noticed that at noon a radio tower on land was due east of the slip. At 1:30pm, the bearing of the tower from the ship was S 35deg E. How far was the ship from the tower at 1:30pm?
*Tuesday, August 3, 2010 at 6:56am by trigofunctions*

**trigo**

in a right triangle XYZ where right angle at angle X, if z= 14 and angle Y = 27.7 degree. Find angle Z, side x and side y.
*Monday, February 21, 2011 at 7:18am by sheosono*

**trigo**

Let the boat be at a distance of s meter from the foot of the cliff. Given, 126/s = tan 20.7 => s = 126/tan 20.7 = 126/0.377 = 334.22 meter.
*Saturday, July 31, 2010 at 11:02pm by Tony*

**Trigo help!**

When I come across an unusual trig identity to prove, the first thing I do is try some arbitrary angle. Since it is an Identity it should be true for any angle e.g. Y = 30º LS = sec30(1+tan30) = appr. 1.821 RS = 6csc30 = 12 No wonder you can't prove it, it is not true !
*Saturday, September 19, 2009 at 9:24am by Reiny*

**trigo**

the front wheel of a bicycle has a diameter of 16 in and the back wheel has a diameter of 26 in. through what angles does the front wheel turn if the rear wheel turns through 24 radians?
*Friday, December 28, 2012 at 12:09am by jane *

**trigo help!**

1. differentiate cos(3/x) 2. differentiate sin(4/x) 3. differentiate 3/{sin(3x+pi)} 4. differentiate pxsin(q/x)where p and q are constants. 5. differentiate xsin(a/x) where a is constant 6. differentiate sec^3(3x^2+1)
*Friday, June 19, 2009 at 8:25am by I'm stumped*

**trigo**

The only hard part I see about this problem is the way the angle is stated. you will have to change it to (23 + 37/60)° and then take the tangent ratio. (on my calculator I have a key labelled D°M'S so I could take tan 23 D°M'S 37 = and I get the same result as above. BTW, did...
*Monday, August 2, 2010 at 6:38am by Reiny*

**trigo**

A television tower stands on the top of the building from point 83.7 feet from the base of the building the angles of elevator to the top and the base of the tower are 63.20 minutes and 38.51 minutes respectively. How tall is the tower?
*Tuesday, October 18, 2011 at 11:09am by jayson austria*

**Trigo!**

I would start this way, cos (2y/3) = -√3/2 so 2y/3 is in quadrants II or III the reference angle is .5236 radians so 2y/3 = pi - .5236 OR 2y/3 = pi + .5236 so y = 3.92699 or y = 5.4978 and the value which falls in your given range of y is 5.4978 or appr. 5.5
*Saturday, September 19, 2009 at 8:35am by Anonymous*

**trigo**

A submarine at the surface of the ocean makes an emergency dive, its path making an angle of 21deg with the surface. a. If it goes for 300 meters along its download path, how deep will it be? What horizontal distance is it from its starting point? b. How many meters must it ...
*Tuesday, August 3, 2010 at 6:49am by trigofunctions*

**MATH TRIGO-PLSSS ANSWER CLEARLY COZ IM VERY LOW IN**

A TOWER AND A MONUMENT STAND ON A LEVEL PLANE.THE ANGLES OF DEPRESSION OF THE TOP AND BOTTOM OF THE MONUMENT VIEWED FROM THE TOP OF THE TOWER ARE 13DEGREE AND 31 DEGREE,RESPECTIVELY;THE HEIGHT OF THE TOWER IS 145 FT. FIND THE HEIGHT OF THE MONUMENT.
*Sunday, March 9, 2014 at 8:49pm by mier*

**trigo**

Let the angle of elevation of the top of the building from a point 1,760 m from the base of the building be P degree. Then, tan P = 1250/1760 = 0.71 tan 36 degrees Hence, the angle of elevation is 36 degrees.
*Saturday, July 31, 2010 at 11:22pm by Tony*

**trigo**

Let the angle of elevation of the top of the building from a point 1,760 m from the base of the building be P degree. Then, tan P = 1250/1760 = 0.71 = tan 36 degrees Hence, the angle of elevation is 36 degrees.
*Saturday, July 31, 2010 at 11:22pm by Tony*

**trigo**

So AC = 5 tan 37° = 5/BC BC = 5/tan37 = ... sin 37° = 5/AB AB = 5/sin 37° = .... b) you were given angle ABC = 37 , so it is found the other angle would be 53°
*Tuesday, July 12, 2011 at 4:12am by Reiny*

**TRIGO HELP!!! NEEDED NOW**

sec^4x - sec^2x = tan^4x + tan^2x
*Friday, December 2, 2011 at 3:06am by NEED HELP NOWW!!*

**trigo**

A space shuttle pilot flying toward the Suez Canal finds that the angle of depression on one end of the canal is 38.25deg and the angle of depression to the other end is 52.75deg. If the canal is 100.6 mi long, find the altitude of the space shuttle.
*Tuesday, August 3, 2010 at 6:44am by trigofunctions*

**trigo**

The 2 lines of sight represent the hypotenuse of 2 rt. triangles, and the height of the hill represents the vertical side of both triangles. The hor. side of smaller triangle(d) is measured from the bottom of hill to A. The hor. side of the larger triangle is = to d + 75m. ...
*Tuesday, August 3, 2010 at 6:28am by Henry*

**Trigo**

Given that a^2+b^2=2 and that (a/b)= tan(45degee+x), find a and b in terms of sinx and cosx. I don't know what i'm supposed to do, and i dont come to an answer! Help, thanks! my workings: tan(45+x)= (1+tanx)/(1-tanx) a/b = (1+tanx)/(1-tanx) a(1-tanx)=b(1+tanx) i square both ...
*Saturday, September 26, 2009 at 1:43am by Marrion*

**Trigo!**

You have done the right step, check your answers after you have squared each side of an equation. Take a simple case of x=-4 square both sides, x²=(-4)²=16 x=√16=±4 check: x=-4 OK x=+4 not a solution. In your case, the solution of 73.126° is correct...
*Saturday, September 19, 2009 at 2:21am by MathMate*

**Trigo**

From a window of a building A, the angle of elevation of the top of building B is 35 degrees and the angle of depression of the bottom of building B is 20 degrees. If the buildings are 25m. horizontally apart, Compute for height of the window from the ground? And compute for ...
*Sunday, March 6, 2011 at 2:15am by Elmo*

**trigo**

A block bordering Sapphire Street is a right triangle. You start walking around the block, taking 125 paces on Sapphire Street and 102 paces on Diamond Street. a. At what angle do Diamond and Sapphire Streets intersect? b. How many paces must you take on Gold Street to ...
*Monday, August 2, 2010 at 6:53am by trigofunctions*

**trigo**

The downward path can be represented by the hypotenuse of a rt. triangle with an angle of 21 deg. between the hypotenuse and hor side. a. Sin21 = Depth/300 Depth = 300 * Sin21 = 107.5m. Hor. Dist. = 300 * Cos21 = 280.1m. b. Dist. = 1000m / Sin21 = 2790.4m.
*Tuesday, August 3, 2010 at 6:49am by Henry*

**trigo**

Draw a diagram. height of building is b height of tower is h tan 63.20° = (b+h)/83.7 tan 38.51° = b/83.7 b = 83.7 * 0.796 = 66.6 (66.6+h)/83.7 = 1.980 h + 66.6 = 165.70 h = 99.1 ft Hmmm. a 99ft tower on a 67ft building?
*Tuesday, October 18, 2011 at 11:09am by Steve*

**trigo**

Scientist estimate the heights of features on the moon by measuring the lenghts of the shadows they cast on the moon's surface. From a photograph, you find that the shadow cast on the inside of a crater by its rim is 325 meters long. At the time the photograph was taken, the ...
*Monday, August 2, 2010 at 6:38am by trigofunctions*

**Trigo help!**

Ok, i've tried this question, and it brings me to no answers. Please help! Prove the following: secY(1+tanY)=6cosecY my workings: LeftHandSide: secY + tanY/cosY = 1/cosY + sinY/cos^2Y =(cosY+sinY)/cos^2Y = ??? How should i attempt this question?? Am i even on the right track? ...
*Saturday, September 19, 2009 at 9:24am by help!*

**trigo**

See response by Mr. Reiny http://www.jiskha.com/display.cgi?id=1244581165
*Tuesday, June 9, 2009 at 5:01pm by MathMate*

**trigo**

Draw a diagram. If the top of the 90m tower is A, the top of the shorter building is B, draw a horizontal line from B to the 90m tower. Label the intersection C. Now, ABC is a right triangle, and angle A is 45°. The difference in heights is side b. The distance between the ...
*Tuesday, October 18, 2011 at 10:58am by Steve*

**trigo**

how do i do this question? a tower stands on top of a cliff. at a distance of 55m from the foot of the cliff, the angles of elevation of the top of the tower as well as the cliff are 60degrees and 45degrees respectively. what is the height of the tower? Draw a figure. Convince...
*Monday, March 12, 2007 at 2:04am by holly*

**TRIGO HELP!!! NEEDED NOW**

you want a proof? sec^4 - sec^2 = sec^2(sec^2 - 1) = sec^2 tan^2 = (tan^2 + 1)(tan^2) = tan^4 + tan^2
*Friday, December 2, 2011 at 3:06am by Steve*

**MATH TRIGO-PLSSS ANSWER CLEARLY COZ IM VERY LOW IN**

Draw a diagram. Let T be the top of the tower M be the top of the monument A be the base of the tower B be the base of the monument ∠TBA = 31° so, 145/TB = sin 31° Since ∠TBM = 59° ∠MTB = 18°, ∠TMB = 103° The desired height (MB) is found by MB/sin18° = ...
*Sunday, March 9, 2014 at 8:49pm by Steve*

**trigo**

An observer at A looks due north and sees a meteor with an angle of elevation of 70deg. At the same instant, another observer 30 miles east of A, sees the same meteor and approximates its position as N 50deg W but fails to note its angle of elevation. Find the height of the ...
*Tuesday, August 3, 2010 at 6:54am by trigofunctions*

**trigo**

A surveyor made the two sections of the railroad bridge, both at 210 meters in length. Suppose that the maximum angle of elevation of each section is 75deg. When the bridge is closed, the water level is normally 13 meters below the bridge. a. When the bridge is fully opened, ...
*Tuesday, August 3, 2010 at 6:35am by trigofunctions*

**trigo**

1. What exponent goes between ^ and cos? If it is 2, I do not believe the identity is valid as written. What IS valid is 1/sin^2 B - sin^2B/(sin^2B cos^2 B) = csc^2 B - sec^2 B or [cos^2 B - sin^2 B]/[sin^2B cos^2B ] = csc^2 B - sec^2 B
*Saturday, December 13, 2008 at 6:52pm by drwls*

**Trigo!**

Ok, i've tried this sum a million times and i cant get an answer. Somebody please check my workings and tell me what i did wrong! Thanks! Given 4≤y≤6, find the value of y for which 2cos((2y)/3) + √3 = 0 Here's my workings: 2.666≤(2y/3)≤4 2cos(2y/3...
*Saturday, September 19, 2009 at 8:35am by help!*

**trigo--help!**

how do i do this question? a ladder length 13m rests against a vertical wall with its foot on a horizontal floor at a distance of 5m from the wall. when the top of the ladder slips down a distance of x, the foot of the ladder moves out x. find the distance of x. a^2 + b^2 = c^...
*Monday, March 12, 2007 at 2:51am by holly*

**trigo**

The pilot travels 200 miles S at 20 deg.-20 min. When he changes direction, he makes a 90 deg angle (20 deg.-20min.) + (69deg.-40 min.) = 90 Deg. During his return path, he completes the rt. triangle. TanA = 200/148 = 1.3514, A = 53.5 deg. B = 90 - 53.5 = 36.5 deg. = 36 Deg,...
*Tuesday, August 3, 2010 at 6:39am by Henry*

**trigo math**

tan*sin+cos = sin^2/cos + cos = (sin^2+cos^2)/cos = 1/cos = sec (tan*cos^2 + sin^2)/sin = (sin*cos + sin^2)/sin = sin(cos+sin)/sin = cos+sin I think you mean (1+tan)/(1-tan) = (1+tan)^2/(1-tan^2) = (1+2tan+tan^2)/(1-tan^2) = (sec^2+2tan)/(1-tan^2) the last one needs some ...
*Thursday, December 13, 2012 at 10:58am by Steve*

**trigo**

sin 47 degree 29 minutes = x/4728 x=4728(sin 47 degrees 29 minutes) x=3484.92m cos 47 degree 29 minutes= y / 4728 y= 4728(cos 47 degrees 29 minutes) y= 3195.20 m Am i correct?
*Tuesday, August 3, 2010 at 6:59am by nick*

**trigo**

The 2 lines of sight represent the hypotenuse of 2 rt. triangles, and the height of the hill represents the vertical side of both triangles. The hor. side of smaller triangle(d) is measured from the bottom of hill to A. The hor. side of the larger triangle is = to d + 75m. ...
*Tuesday, August 3, 2010 at 6:28am by Henry*

**Trigo**

1. cos^sup2;(x)-cos(2x) = 0 (1-sin²(x)) - (cos²(x)-sin²(x)) = 0 (1-sin²(x)) - cos²(x) + sin²(x) = 0 1-cos²(x) = 0 sin²(x) = 0 On the interval [0,2π], sin²(x) = 0 at x=0, π and 2π Subsititute x=0, π and 2π into the ...
*Wednesday, June 2, 2010 at 8:52am by MathMate*

**TRIGO**

take the derivative and set that equal to zero let y = 9tan^2 x + 4cot^2 x dy/dx = 18tanx(sec^2x) + 8cotx(-csx^2x) = 0 18(sinx)/(cosx)(1/cos^2x) + 8(cosx/sinx)(-1/sin^2x) = 0 18sinx/cos^3x) - 8cosx/sin^3x = 0 18sinx/cos^3x) = 8cosx/sin^3x 18sin^4x = 8cos^4x sin^4x/cos^4x = 8/...
*Friday, June 3, 2011 at 5:25am by Reiny*

**trigo**

Tan52.75 = h/d. d = hor. dist. from shuttle to canal. h = d*Tan52.75 = Altitude of shuttle. Tan38.25 = h/(d+100.6) h = (d + 100.6)* Tan38.25 Substitute d * Tan52.75 for h: d*Tan52.75 = (d + 100.6)*Tan38.25 Solve for d: 1.3151d = 0.7883d + 79.31 1.3151d - 0.7883d = 79.31 0....
*Tuesday, August 3, 2010 at 6:44am by Henry*

**trigo math**

7. Prove that tan B sin B + cos B = sec B. 11. Prove that tanλ cos^2λ +sin^2λ/sinλ = cos λ + sin λ. 12. Prove that 1+tanθ/1+tanθ = sec^2θ+2tanθ/ 1-tan^2θ. 21. Prove that sin^2w-cos^2w/ tan w sin w + cos w tan w = cos...
*Thursday, December 13, 2012 at 10:58am by RUDY*

**calculus 2**

∫ (63x(cos(x))^2) dx 63 ∫ x(cos(x))^2 dx Recall that cos^2 x is also equal to (1/2)(1+cos(2x)): 63/2 ∫ x(1+cos(2x)) dx 63/2 ∫ x + x cos(2x) dx First term is easy, it becomes: 63/2 ∫ x dx = (63/4)x^2 For the second term, we use integration by parts...
*Friday, September 6, 2013 at 9:30pm by Jai*

**trigo**

Oops!! I missed a part of the problem during my 1st response. (-1.2X^6 -0.018X^5 +4.2X^2) / -6X^4 Divide each term by -6X^4: 2X^2 0.003X -0.7/X^2. Remember to subtract the exponents when dividing. The last term of the answer had a negative exponent. So it was moved to the ...
*Monday, July 26, 2010 at 6:12am by Henry*

Pages: **1**