Download Trigonometric Functions of General Angles

Honors Analysis
Section 7.2: Trigonometric Functions of General Angles
Q Problems
Q1.) How many committees of 4 people can be selected from a group of 6 people?
Q2.) How many ways can 5 students be seated around a circular table?
Q3.) What is the probability of rolling a sum of 8 on two fair, six-sided dice?
Q4.) A linear function exists such that f(0) = 20 and f(4) = 0. What is f(10)?
Q5.) 5−3 =
Q6.) Convert 45 mph to ft/s.
Q7.) What is the GCF of 28352 and 8960? (Hint: Use the prime factorizations!)
Q8.) What is the LCM of the numbers from Q7?
Q9.) Benji rode his bike 30 miles. If he increased his speed by 3 mph, he would have decreased his travel time by 20
minutes. What was his original speed?
Q10.) Solve for y:
1.) Give the algebraic definitions of the six trigonometric functions when graphed in standard position on the coordinate
plane (use x, y, and r, where 𝑟 = √𝑥 2 + 𝑦 2 ).
Give the exact values of the six trigonometric functions of angle 𝜃 if the terminal side of the angle contains the given
point.
2.) (3, -4)
3.) (-15, 8)
4.) (7, 24)
5.) (6, 6)
6.) (-4, 0)
7.) (2, 4)
Sketch each angle in standard position. Then determine its reference angle.
5𝜋
8.) 250º
9.) 140º
10.) -240º
11.) 4
12.)
Determine the exact value of each trig function:
13.) sin 150º
14.) cos 300º
15.) tan 135º
16.) cos 180º
19.) tan 90º
20.) sec
17.) 𝑐𝑜𝑠
5𝜋
6
18.) tan
7𝜋
4
21.) tan
5𝜋
3
22.) cot 510º
23.) cos
11𝜋
3
2𝜋
3
7𝜋
6
24.) csc 450º
Suppose 𝜃 is an angle in standard position whose terminal side is in the given quadrant. For each function, find the exact
values of the remaining five trigonometric functions of 𝜃.
3
12
8
25.) cos θ = 5, Quadrant 1
26.) tan 𝜃 = − 5 , Quadrant II
27.) sin θ = 17 , Quadrant II
1
28.) cot 𝜃 = 2 , Quadrant III
29.) sec 𝜃 = −√10, Quadrant IV
30.) csc 𝜃 = −5, Quadrant IV
Given that angle 𝜃 is graphed in standard position, state the quadrant or quadrants in which the terminal side lies:
31.) sin 𝜃 > 0
32.) tan 𝜃 < 0
33.) sin 𝜃 > 0, cos 𝜃 < 0
34.) tan 𝜃 > 0, cos 𝜃 < 0
Find two values of x that make each statement true:
35.) cos x = 1
36.) sin x = 1
37.) cos x = 0
38.) sin x = 0
39.) cos x = -1