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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

Find the approximate value of each trigonometric function 31 Given that tano 3454 where ltlt find the values of sine and cose If necessary round to 3 2 decimal class=

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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

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