Trigonometry
posted by Cassie .
a. Find the exact value of
sin (theta  pi/6)
b. Find the exact value of
cos (theta  pi/4)
c. For what numbers x, 2pi less than or equal to x less than or equal to 2pi does cos x = 1
d. What is the range of the cosine function?
e. For what numbers x, pi less than or equal to x less than or equal to pi is the graph of y = cos x increasing?
f. Given: tan alpha = 4/3,
pi/2 < alpha , pi and
cos beta = 1/2, 3pi/2 < beta , 2 pi.
Find: tan (alphabeta)

a.
sin(theta)= sin(theta)
sin(pi/6)=  sin(pi/6)= 1/2
b.
cos(theta)=cos(theta)
cos(pi/6)=cos(pi/6)= sqroot(3)/2
c.
pi
d.
The cosine function, like all of the trigonometric functions, is periodic about the rotation around a circle. Since the cosine is defined as the adjacent/hypotenuse of a right triangle, you can clearly see that its value can never be greater than one or less than 1 since the hypotenuse is always longer than the adjacent side. It turns out that, indeed, the cosine's range is from 1 to 1, written [1,1].
e.
pi/2,pi