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10 votes
Parabola

Given that tanθ=
-(9)/(4) and
(\pi )/(2\\)<θ<π , find the exact values of the trigonometric functions.

User Andrew Corrigan
by
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1 Answer

10 votes
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Answer:

  • sin(θ) = (9√97)/97
  • cos(θ) = (-4√97)/97
  • csc(θ) = (√97)/9
  • sec(θ) = (-√97)/4
  • cot(θ) = -4/9

Explanation:

The angle is in the 2nd quadrant, where the sine is positive and the cosine is negative.

tan^2(θ) +1 = sec^2(θ) = (-9/4)^2 +1 = 97/16 ⇒ sec = -(1/4)√97

cot(θ) = 1/tan(θ) = -4/9

csc^2(θ) = cot^2(θ) +1 = (-4/9)^2 +1 = 97/81 ⇒ csc = (1/9)√97

sin(θ) = 1/csc(θ) = (9√97)/97

cos(θ) = 1/sec(θ) = (-4√97)/97

User Sultana
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