# Pre calc

Given that tanθ = 2 root 10 over 9 and cscθ < 0 , find the exact value of cos(θ − pie over 4) .

I solved for the other side and got 11. After this idk what to do I was thinking using
cos(a-b)=cos(a)cos(b)-sin(a)sin(b) but idk how to witht the pie/4 someone please help

1. 👍 0
2. 👎 0
3. 👁 62
1. tanØ = 2√10/9
recall tanØ = y/x in the corresponding right-angled triangle
we are also given that cscØ is negative, so Ø must be in III

then y = -2√10 and x = -9
r^2 = 40 + 81 =121
r = 11

x = -9, y = -2√10, r = 11
sinØ = -2√10/11, cosØ = -9/11

cos(Ø - π/2)
= cosØcos π/2 + sinØsin π/2
= (-9/11)(0) + (-2√10/11)(1)
= -2√10/11

π/2 radians = 90°
You should know the trig functions of sine, cosine, and tangents of the main angles .
30°, 60°, 90° from the standard right-angled triangle with corresponding sides 1 : √3 : 2
and the 45 - 45 - 90 triangle with sides
1 : 1 : √2
trig functions of 0, 90, 180 270 and 360 you should know by looking at their curves.

1. 👍 0
2. 👎 0
posted by Reiny
2. well, the sides could be 1, (2/9)sqrt10 and hypotenuse 11/9

or
9, 2 sqrt 10, 11 with 2 sqrt 10 opposite θ

we know sin θ <0 so θ in quadrant 3 or 4
since tan is +, must be quadrant 3

now actually
cos(a-b)=cosa cosb + sina sinb
cos a = 9/11
cos b = 1/sqrt 2
sin a = -(2/11) sqrt10
sin b = 1/sqrt2
so
9/(11 sqrt 2) - (2/11)sqrt 5
sin a = -2 sqrt 10

1. 👍 0
2. 👎 0
posted by Damon
3. but she said pi/4 :)

1. 👍 0
2. 👎 0
posted by Damon
4. oh, cos also - in quadrant 3
cos a = -9/11

1. 👍 0
2. 👎 0
posted by Damon

## Similar Questions

1. ### precalculus

#1 cscθ-cotθ #2 cosθ(tanθ-secθ) #3 tanθ+sinθ/cscθ+cotθ

asked by lucy on November 25, 2012
2. ### Math Question

Find the values of the six trigonometric functions of an angle in standard position where the terminal side is going through the point (-1, 1). Sinθ = Cosθ= Tanθ= Cscθ= Secθ= Cotθ=

asked by Todd on December 4, 2014
3. ### Precalc/Trig

Sorry there are quite a few problems, but I just need to know if these are correct (and if they aren't, where I went wrong): 1. Solve these equations. tanθ = -√3 θ = 2π/3 + kπ θ = 5π/3 + kπ 2. secθ = √2 θ = π/4 +

asked by Heather on November 11, 2014
4. ### math trigono

1. If tanθ = –√3 , what is the value of cot ? 2. Find the value of 3sec2.4. (Round to the nearest tenth.) 7. if θ is a standard position angle and cotθ = 1.85, in which quadrant(s) could θ lie? 14.if sinθ = -4/5 and

asked by Stan on December 12, 2012
5. ### Math

Hi! Can someone help me with these? I'm suppose to verify each idenity. Thanks! 1.) 1/tanθ +tanθ=sec^2θ/tanθ 2.) secθ-1/1-cosθ=secθ

asked by Lori on January 19, 2015
6. ### trigonometry

tanθ= -2sqrt10/3 and π/2

asked by Yulieth on November 20, 2011
7. ### Trig

Verify the given equations: ____1______ + ____1_______ = -2 tanθ tanθ – secθ tanθ + secθ 1 – sinθ = sec2θ – 2 secθ tan θ + tan2θ 1 + sinθ

asked by McKenna Louise on February 28, 2014
8. ### Trig

Solve the trig equation exactly over the indicated interval. tanθ = 0, all real numbers I know the answer is πn, but I don't understand how they got this. I get that tanθ = 0 on π and 2π on the unit circle, so did they just

asked by Anne on April 7, 2013
9. ### Trigonometry

Given that sin(2/(√229))and that 0∘0∘ < θθ < 90∘90∘, with the aid of a diagram and without the use of a calculator determine: a) cosθcos⁡θ = b) tanθtan⁡θ = c) tanθ÷cscθtan⁡θ÷csc⁡θ = d)

asked by Boitshepo on May 24, 2018
10. ### physics

Two charged spheres of charge q and mass m are each hanging from strings and are at equilibrium as shown below: Give an expression for tanθ in terms of ke (use "k" to write ke), q, m, g (gravity), and d (the distance between the

asked by Anonymous on January 20, 2014

More Similar Questions