trigonometric functions

Question

Find two solutions of the equation. Give your answers in degrees (0° ≤ 𝜃 < 360°) and radians (0 ≤ 𝜃 < 2𝜋). Do not use a calculator. (Do not enter your answers with degree symbols.)

(a)    cot(𝜃) = 0

degrees:

radians:

b) sec(𝜃) = - sqrt 2

degrees

radians

Answer 1

a) cot(theta) = 0

cotangent(theta) = adjacent side/opposite side= 0/1 for a unit circle,

theta = pi/2 or 3pi/2 radians or

90 or 270 degrees

b) sec(theta) = -sqr2

sec(theta) = 1/cos(theta) =-sqr2

cos(theta) = 1/-sqr2 = -sqr2/2

sqr2/2 is the cosine of 45 degrees. It's negative sqr2/2 in quadrants II and III

where theta = 180 + and - 45 = 135 and 225 degrees or

theta = pi + or - pi/4 = 5pi/4 or 3pi/4 radians