PRE CALCULUS Trigonometry 5

Question 1

The area of a triangle with sides a = 7, b = 9, and included angle C = 60° is:

Accepted Answer

63√3/4

Answer

Area = (1/2)ab·sin(C) = (1/2)(7)(9)·sin(60°) = (63/2)(√3/2) = 63√3/4.

Question 2

Which of the following represents a half-angle formula for cos(θ/2)?

Accepted Answer

±√((1 + cosθ)/2)

Answer

The half-angle identity for cosine is cos(θ/2) = ±√((1 + cosθ)/2).

Question 3

For y = -2cos(x) + 1, what is the vertical shift and reflection?

Accepted Answer

Shifted up 1 unit and reflected over the x-axis

Answer

The coefficient -2 reflects the graph over the x-axis, and the +1 shifts it up 1 unit.

Question 4

In which quadrant is an angle θ if sin(θ) > 0 and tan(θ) < 0?

Accepted Answer

Quadrant II

Answer

Sine is positive in Q1 and Q2; tangent is negative in Q2 and Q4; the overlap is Quadrant II.

Question 5

What is the simplified form of sin(x)·cot(x)?

Accepted Answer

cos(x)

Answer

sin(x)·cot(x) = sin(x)·(cos(x)/sin(x)) = cos(x).

PRE CALCULUS Practice Test