Find the exact value of each expression if 0 degrees < theta < 90 degrees

Question

If tan (theta) = 1/2 , find cos(theta)
If cos(theta) = 8/17, find csc (theta)

Find the exact value of each expression is 180 degrees < theta < 270 degrees
7. If tan (theta)= 1, find cos(theta)

Answer 1

Tangent is opposite / adjacent, so we can say that in tan (theta) = 1/2, the 1 and 2 are the sides of the right triangle and
c^2 = a^2 + b^2
c^2 = 1^2 + 2^2
c = sqrt(5) is the hypotenuse.

Cosine is adjecent / hypotenuse, so
cos(theta) = 2 / sqrt(5)

Method is the same for other questions.