Question

cos(θ)= 1/6Trig: use the given function value and the trigonometric identities to find the exact value of each indicated trigonometric function.a. Sin (θ)b. Tan (θ)c. Sec (θ)d. Csc (90° -θ)

Answer 1

Answer:

a. Sin (θ) = √35 / 6

b. Tan (θ) = Tan θ = √35

c. Sec (θ) = 6

d. Csc (90° -θ) = 6

Explanations:

Note that according to trigonometric identities:

cos θ = Adjacent / Hypotenuse

From the question:

cos θ = 1/6

Comparing this with the given trigonometric identity:

Adjacent, A = 1

Hypotenuse, H = 6

Let us look for the opposite, O

Using the pythagora's theorem

H² = A² + O²

6² = 1² + O²

36 = 1 + O²

36 - 1 = O²

O² = 35

O = √35

Therefore, Opposite = √35

a) Sin θ = Opposite / Hypotenuse

Sin θ = √35 / 6

b) Tan θ = Opposite / Adjacent

Tan θ = √35 / 1

Tan θ = √35

c) Sec θ = 1 / cos θ

Sec θ = 1 ÷ 1/6

Sec θ = 1 x 6

Sec θ = 6

d) Csc ( 90 - θ) = Sec θ

Since Sec θ = 6

Csc ( 90 - θ) = 6