# Precalc

Find the values of x between (or equal to) 0 and 360 degrees to satisfy each equation.

arcsin1/2=x
I got 30 degrees as one angle, but how do I find the second one?

arccot1=x

Also,

Find each value:

arccos(-1/2)

and

sin(2 sin^-1 1/2)

Thanks in advance. Even a little help is appreciated.

1. 👍
2. 👎
3. 👁
1. ALWAYS draw the problem
sketch your origin and x,y axes
now you can see that for a unit hypotenuse, the opposite side (y) is positive in guadrants one and two,\.
so 30 degrees is one answer
and 30 degrees above the -y axis is the other place where sin = 1/2
that is of course 180 - 30 = 150 degrees

now if cotangent is one, tangent is one.
so sure, 45 degrees will do.
BUT where else is y/x positive?
It is where both x and y are negative, quad 3
so 180 + 45 = 2556 is second answer

I think you can take it from there. Sketch your four quadrants and then your x and y

1. 👍
2. 👎
2. sines are positive in the first and second quadrant. If sin A = 1/2, A can be wither 30 or 150 degrees. The absolute value of sin, cost and tan etc. are determined by the angle with the horizontal axis.

cot and tan are negative in the second and fourth quadrants, and positive in the first and third quadrants.
cot^-1(1) = 45 or 225 degrees

cosine is negative in second and third quadrants.
cos-1(-1/2) = 120 and 240 degrees (60 degrees from the -x axis)

sin(2 sin^-1 1/2) = sin 2*30 or sin 2*150 = +0.866 or -0.866, since there are twqo possible values for sin^-1 (1/2)

1. 👍
2. 👎
3. "arcsin1/2=x

I got 30 degrees as one angle, but how do I find the second one?"

There is only one angle and it is 30 degrees. Don't confuse arcsin(1/2) with the set of the solutions of the equation sin(x) = 1/2.

It is similar to solving the equation:

x^2 = 4

and the squareroot function, in this case sqrt(4). The solution of the equation x^4 = 4 is not unique, there are two solutions: x = 2 and x = -2. So, there are two possible inverse functions that one can define. One has to make some choice. The squareroot function is defined as the postive solution of the equation. So sqrt(4) = 2 and not -2.

You can imagine what a terrible mess it would be if the two possible definitions were both used.

Similarly, one has defined the arcsin function such that it gives ONE of the solutions of the equation
sin(x) = y. By definition arcsin(y) is that solution of sin(x) = y that lies in the range between -pi/2 and pi/2.

1. 👍
2. 👎

" Find the values of x between (or equal to) 0 and 360 degrees to satisfy each equation.

arcsin1/2=x "

Which is not exactly what is arcsin(1/2)

1. 👍
2. 👎

## Similar Questions

1. ### inverse trig HELP PLEASE!!

Write the general solution to y = arcsin (0.6428). 40°±360°k 140°±360°k 220°±360°k 320°±360°k How do I find the right answer? I am like seriously stuck. I need help please.

2. ### math

solve the equation for the range zero degrees less than or equal to theta less than or equal to 360 degrees. 4 sin 0=-1

3. ### Calculus

Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function. If there are multiple values, separate them with commas; enter N if there are no such values. f(x)= x^2-10x+3, [0,10]

4. ### trig

what are the values of theta in the interval 0 degrees is lessthan or equal to theta is less than or equal to 360 degrees that satisfy the equation tan theta minus square root of 3 equals 0?

1. ### trigonometry

Find all the angles between 0 degrees and 360 degrees which satisfy the equations a. 8 cos x sin x = sin x b. 5 tan^2 y + 5 tan y = 2 sec^2 y.

2. ### trig

Solve the equation 2 tan C - 3 = 3 tan C-4 algebraically for all values of C in the interval 0 degrees

3. ### trig

how do you find all the values of theta from 0 degrees through 360 degrees for which sin theta equals 0

4. ### Math/Trig

Solve: 2 sin x - 1 = 0 for 0 degrees is less than or equal to x is less than 360 degrees.

1. ### Geometry

Please Someone Help!!! Find the coordinates of a point on the unit circle corresponding to a 36 degree angle rotation. Find the coordinates of a point on the unit circle corresponding to a 115 degree angle of rotation. Find all

2. ### Algebra 2 Honors

Find all solutions if 0 degrees is less than or equal to x and x is less than 360 degrees. 2 sin^2(x)+ sin(x)=1

3. ### Algebra 2

The formula A = 180(n-2)/n relates to the measure A of an interior angle of a regular polygon to the number of sides n. If an interior angle measures 120 degrees, find the number of sides A)5 B)6 C)8 D)10 I have NO clue on how to

4. ### math

find the angle that is coterminal to 525 degrees and lies between 0 degrees and 360 degrees? 165 degrees 255 degrees 195 degrees 345 degrees