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pls help!!! Let theta equals negative 9 times pi over 4 period


Part A: What is a coterminal angle of θ such that 0 ≤ θ ≤ 2π? (5 points)


Part B: What are the exact values of all six trigonometric functions evaluated at θ?

Sagot :

Lanuel

A coterminal angle of θ such that 0 ≤ θ ≤ 2π is equal to 7π/4 and the exact value of Sin(θ) = -1/√2.

What is a coterminal angle?

A coterminal angle can be defined as an angle that share the terminal side of an angle which occupies the standard position i.e it has the same initial side.

In this scenario, all angles that are multiples of 2π and added to the given angle (-9π/4) would be coterminal. For the range [0, 2π], 8π should be added to the given angle as follows:

Coterminal angle = -9π/4 + 4π

Coterminal angle = -9π/4 + 16π/4

Coterminal angle = 7π/4.

Part B.

The reference angle is given by:

7π/4 -π = 3π/4.

Therefore, the exact values of all six (6) trigonometric functions evaluated at θ are:

  • Sin(θ) = -1/√2.
  • Cosec(θ) = √2.
  • Cos(θ) = 1/√2
  • Sec(θ) = -√2.
  • Tan(θ) = -1.
  • Cot(θ) = -1.

Read more on coterminal angles here: https://brainly.com/question/23093580

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