PRE CALCULUS Pre-Calculus Trigonometry 5

Question 1

What is the inverse sine (arcsin) of −1?

Accepted Answer

−π/2

Answer

arcsin(−1) = −π/2 because sin(−π/2) = −1 and −π/2 is in the restricted range [−π/2, π/2].

Question 2

In a triangle with sides a = 7, b = 10, and included angle C = 60°, what is the value of c²?

Accepted Answer

79

Answer

By the Law of Cosines: c² = 7² + 10² − 2(7)(10)cos60° = 49 + 100 − 70 = 79.

Question 3

What is the phase shift of y = cos(2x + π)?

Accepted Answer

π/2 to the left

Answer

Rewrite as cos(2(x + π/2)); the phase shift is π/2 units to the left.

Question 4

Which of the following angles is co-terminal with −45°?

Accepted Answer

315°

Answer

Adding 360° to −45° gives 315°, which is co-terminal.

Question 5

What does the identity 1 + cot²θ = csc²θ follow from?

Accepted Answer

Dividing sin²θ + cos²θ = 1 by sin²θ

Answer

Dividing every term of sin²θ + cos²θ = 1 by sin²θ yields 1 + cot²θ = csc²θ.

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