Use 90°<θ<180° and sin θ=24/25 ⁡to answer the following questions. Part A: What is cos⁡ θ? Part B: What is cot⁡ θ?

Answer 1

a) We using Pythagorian Identity: sin²θ + cos²θ = 1, (24/25)²+ cos²θ = 1.

From here cos²θ = 1 - 576/625, cos²θ = 49/625 and cosθ = - (49/625)^1/2 = - 7/25.

We choose minus because in 2nd quadrant cosine negative

b) cotθ = cosθ/sinθ = (-7/25)/(24/25) = - 7/24

Answer 2

sin=opposite/hypotenuse and cos=adjacent/hypotenuse

sinθ=24/25

so, 25^2=24^2+"adjacent^2"

625=576+"adjacent^2"

625-576="adjacent^2"

49=adjacent^2

√49=7

adjacent=7

cosθ=-7/25

tan=sin/cos

cot=cos/sin

cotθ=(7/25)/(24/25)

cotθ=-7/24