Trigonometry Exam 1 Review

Determining θ

100

Determine the quadrant in which θ lies when cosθ < 0 and cotθ > 0

Quadrant III

200

Convert 3π/10 to degrees.

54^o

300

Determine the reference angle θ' of the angle θ = 205^o

θ' = 25^o

400

State two exact values of θ in degrees (0^o < θ < 360^o) such that cos(θ) = -√(3) / 2

θ = 150^o and 210^o

500

Determine two coterminal angles (one positive and one negative) to 5π/4

positive coterminal = 13π/4

negative coterminal = -3π/4

Transforming Graphs

100

What is the period and amplitude of y = (5/2)sin(x)

period = 2π

amplitude = 5/2

200

What is the period of y = tan(x/3)

3π

300

The point (π, -1) is on the graph of y=cos(x).

What transformed point will be on the graph of y=3(cos x + π)

(0, -3)

Shift left π units, and vertically stretch by a factor of 3

400

The point (π/2, 1) is on the graph of y = sin(x)

What transformed point will be on the graph of y=5+sin(πx)

(1/2, 6)

Horizontal shrink, and shift up 5 units.

500

What is the range of the graph of y=4sin(x)

[-4, 4]

Finding Trig Function Values

100

What is the exact value of:   cos(5π/2)

0

200

What is the exact value of:  csc(3π/4)

√2

300

An acute angle θ is within a right triangle. The length of the side adjacent to θ is 24. The length of the side opposite to θ is 7.

Determine the exact value of cosθ

24/25

400

The point (3, -4) is on the terminal side of an angle in standard position.

Determine the sine value of the angle.

sinθ = -4/5

500

Determine the exact value of tanθ given:

cscθ = 3/2    and cosθ < 0

tanθ = -2√5 / 5

Solving Right Triangles

100

Given the following values of a right triangle:

A = 8.4^o,     a = 40.5

Solve for angle B. (State the answer in degrees rounded to three decimals)

B = 90^o - 8.4^o = 81.6^o

200

Given the following values of a right triangle:

a = 2,    c = 6

Solve for side b. (Rounded to three decimals)

b = √32 = 5.657

300

Given the following values of a right triangle:

B = 72.8^o,     a = 4.4

Solve for side b. (rounded to three decimals)

b = 4.4tan(72.8^o) = 14.214

400

A football lands at the edge of the roof of your school building. When you are 25 feet from the base of the building, the angle of elevation to the football is 21^o. How high off the ground is the football?

Round the answer to three decimal places.

25tan(21^o) = 9.597 ft

500

The height of an outdoor basketball backboard is 12.5 feet, and the backboard casts a shadow 17 feet long. What is the angle of elevation from the tip of the shadow to the top of the backboard? (State answer in degrees rounded to three decimal places.)

tan^-1(12.5/17) = 36.327^o