Unit 5 Review! Created by Educational Technology Network. www.edtechnetwork.com 2009

Trig Functions Angles and Things Trig with angles Periodic Functions Extra Trig Stuff 10 20 30 40 50

Trig Functions - 10 Find sin, cos, and tan of the following triangle 5 3 θ 4

Answer – 10 Sinθ = 3/5 Cosθ = 4/5 Tanθ = 3/4

Trig Functions - 20 If sinθ = 6/7, find the third side of the triangle. c a θ b

Answer – 20 b = √13 c a θ b

Trig Functions - 30 Find θ to the nearest degree. 5 θ 13

Answer – 30 θ = 22.62* 5 θ 13

Trig Functions - 40 Given the point (3, 2), sketch the angle and find csc of θ.

Answer – 40 Cscθ = √13 / 2 √13 2 θ 3

Trig Functions - 50 Find tanθ given that sinθ = - ¾, 180 < θ < 270

Answer – 50 tanθ = √5 / -3 θ

Angles and Things - 10 Which best describes the relationship between these angles? a. The angle measures are equal b. The angles are opposite each other c. The angles have equal sines d. The angles have equal cosines (-x, y) (x, y)

Answer – 10 c. The angles have equal sines (-x, y) (x, y)

Angles and Things - 20 Find two different angles coterminal with 3π/2

Answer – 20 Answers may vary. Ex.’s: 7π/2, -π/2

Angles and Things - 30 Convert 7π/6 to degrees.

Answer – 30 210*

Angles and Things - 40 Which quadrant is 865 degrees in?

Answer – 40 Quadrant II 865 – 360 – 360 = 145

Angles and Things - 50 Graph 16π/5.

Answer – 50

Trig with angles - 10 Given that the figure represents the unit circle, what is the cosine of r? (√3/2, 1/2) r

Answer – 10 cos(r) = √3/2 (√3/2, 1/2) r

Trig with angles - 20 What is the reference angle of 4π/7 in radians?

Answer – 20 3π/7

Trig with angles - 30 What is the radian measure of the point on the unit circle at (-√3 /2, -1/2)?

Answer – 30 7π/6

Trig with angles - 40 What is the reference angle of 189 degrees?

Answer – 40 9 degrees

Trig with angles - 50 What is the coordinate point (x, y) of 315*?

Answer – 50 (√2 /2, -√2 /2)

Periodic Functions - 10 What is the amplitude for the equation y = 4cos(3x) - 2

Answer – 10 4

Periodic Functions - 20 Given the graph, what is the period? -10 -5 0 5 10 15

Answer – 20 5

Periodic Functions - 30 Given the equation y = 3sin(4θ) -1, what is the frequency?

Answer – 30 2/π

Periodic Functions - 40 In △FGH, ⦟G = 90*, g = 5, and f = 4. What is the measure of angle H?

Answer – 40 ⦟H = 36.87* F 5 G H 4

Periodic Functions - 50 Create an equation for the graph below

Answer – 50 6cos(πθ/3)+ 2

Extra Trig Stuff - 10 A 35ft rope is attached to the top of a telephone pole to keep it upright during storms. If it makes an angle of elevation of 60*, how far away from the pole is the anchor spot?

Answer – 10 17.5ft 35 60* x

Extra Trig Stuff - 20 What is the reference angle to 631 degrees?

Answer – 20 89 degrees

Extra Trig Stuff - 30 Using the Pythagorean Identity sin2θ + cos2θ = 1 Find sinθ if cosθ = 2/3 and θ is in Quadrant I.

Answer – 30 √5 / 3

Extra Trig Stuff - 40 Using the Pythagorean Identity, find tanθ if sinθ = -3/4 and 180 < θ < 270

Answer – 40 -√7 / -4 or √7 / 4

Extra Trig Stuff - 50 What is the difference between period and frequency?

Answer – 50 Period is the length of one cycle, frequency is the amount of cycles per unit of time. For an extra 10 points, what are the equations for these two? Period = 2π/b Frequency = b/2π