Question

Find the approximate value of each trigonometric function.

Answer 1

IDENTITY:

sinθ = - tanθ/√(1 + tan²θ)

cosθ = - 1/√(1 + tan²θ)

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ANSWER:

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

sinθ = - 3.454/√(1 + 3.454²)

• - 0.961

cosθ = - 1/√(1 + 3.454²)

• - 0.278

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Answer 2

Answer:

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