Question

Find the exact expressions for sin theta, cos theta, and tan theta. sin theta = (Simplify your answer) cos theta = (Simplify your answer) tan 0 = (Simplify your answer)

Answer 1

The answers to your questions are given below.

Explanation:

Data obtained from the question include:

Opposite = b

Adjacent = a

Hypothenus = c

Sin θ =..?

Cos θ =.. ?

Tan θ =..?

A. Determination of Sin θ

Sin θ = Opposite /Hypothenus

Opposite = b

Hypothenus = c

Sin θ = Opposite /Hypothenus

Sin θ = b/c

B. Determination of Cos θ

Cos θ = Adjacent / Hypothenus

Adjacent = a

Hypothenus = c

Cos θ = Adjacent / Hypothenus

Cos θ = a/c

C. Determination of Tan θ.

Tan θ = Opposite/ Adjacent

Opposite = b

Adjacent = a

Tan θ = Opposite/ Adjacent

Tan θ = b/a

D. Simplification of Sin θ = Cos(90 – θ)

Recall:

Cos (A – B) = CosACosB + SinASinB

Cos(90 – θ) = Cos90Cosθ + Sin90Sinθ

Therefore,

Sin θ = Cos(90 – θ)

Sin θ = Cos90Cosθ + Sin90Sinθ

But:

Sin θ = b/c

Cos 90 = 0

Cos θ = a/c

Sin 90 = 1

Sin θ = Cos90Cosθ + Sin90Sinθ

b/c = 0 x a/c + 1 x b/c

b/c = b/c