Question

Find the approximate value of each trigonometric function.

31
Given that tano 3.454 where << find the values of sine and cose. If necessary, round to 3
2
decimal places.
In Quadrant III, sino s
and cost

Answer 1

Given

• tanθ = 3.454
• θ is in the III quadrant

We know in the III quadrant both sine and cosine are negative.

Use the following identities to get values of sinθ and cos θ

• sinθ = - tanθ/√(1 +tan²θ)
• cosθ = - 1/√(1 +tan²θ)

Substitute the value of tanθ and find sine and cosine:

• sinθ = - 3.454/√(1 + 3.454²) = - 0.961
• cosθ = - 1/√(1 + 3.454²) = - 0.278