find the following exact value?

Question

a-sin(5π/3)

b-cos(-7π/6)

c-cot(7π/4)

d-csc(-13π/2)

Answer 1

a-sin(5π/3) = -{sqrt(3)}/2

b-cos(-7π/6) = -{sqrt(3)}/2


c-cot(7π/4) = -1
d-csc(-13π/2) = -1

Answer 2

I'll show you how to the first one and you try the others.

First, you must know that pi radians is the same angle as 180 degrees going counterclockwise from the positive x-axis.

pi/3 radians would be the same as 1/3 of 180 degrees of 60 degrees.

So step of 5pi/3 which is pi + 2/3 pi radians, or 180 degrees + 60 degrees + another 60 degrees. This angle has the same terminal side as -pi/3 radians or -60 degrees.

Once you find the terminal side go out 1 unit on it and mark a point. Now drop a perpendicular from this point to the x-axis and darken the segment from the point where it intersects the x=axis back to the origin.

If you have not done so you need to memorize that on a unit circle the triangle you have drawn has sides of x=1/2 and
y = -sqrt(3)/2 where we use negative here because we want the coordinates of the point on the unit circle where the terminal side of 5pi/6 terminates.

By definition sin(5pi/3) = y (on unit circle) = -sqrt(3)/2


Trig is not easy if you don't learn the definitions, how to make diagrams, and how to determine the coordinates of points on the unit circle. You can get all the help you want but until you take the time to do these things you will never master trig.

Answer 3

The thete values are in radian measure, but you may be more confident in degree measure.

sin (300) = -sin (60) = -sqrt(3) / 2

cos ( -210) = -cos (30) = -sqrt(3)/2

cot ( 315) = 1/ tan (-45) = -1

csc( -1170) = 1 / sin (-90) = -1 / sin (90) = -1

Answer 4

a-sin(5π/3) = sin(-pi/3) = - sin(pi/3) = -sqrt(3)/2

b-cos(-7π/6) = cos(5pi/6) =-cos(pi/6) = -sqrt(3)/2

c-cot(7π/4)= cot(-pi/4)=-cot(pi/4 = -1

d-csc(-13π/2)= csc(-pi/2) =-csc(pi/2) = -1

Answer 5

2(pi) radians = 360 degrees.
So 5/3(pi) radians are 300 degrees
-7/6(pi) radians are -210 degrees
7/4(pi) radians are 315 degrees
-13/2(pi) radians are -1170 degrees

Answer 6

a.) -(sqroot3)/2
b.) -(sqroot3)/2
c.) -1
d.) 1

found all of them using the unit circle

Answer 7

Have you lost you scientific calculator?
I can't do these in my head!!!!