1. Solving Trig Functions
Unit 5 Day 9
Solving Trig Functions

2. Warm-up Day 9 x = 61.04 ft (cos) x = 22.35 ft (sin)
A water skier must be at least a horizontal distance of 50 feet from the boat in order to safely avoid undertow from the propeller. If the angle of elevation is 35° from the skier to the pole how long is the rope? (round to nearest hundredth)
2. A 21-foot tree needs trimming. Safety guidelines say the angle made by the ladder and the ground should be 70°. How long should the ladder be to reach the top of the tree?
(round to nearest hundredth)
x = ft (cos)
x = ft (sin)

3. Homework Answers x = 41.4 m Sin A = 15/17 Cos A = 8/17 Tan A = 15/8
Angle B = 66 ⁰
a = 4.5
c = 10.9
x = 41.4 m
x = ft

4. Homework Answers Angle A = 33⁰ c = 26.9 a = 14.9 Angle A = 6. 6 ⁰
Angle C = 40.4 ⁰
b = 10.99
Angle A = 33⁰
c = 26.9
a = 14.9
Angle A = 27.7 ⁰
Angle B = 40.5 ⁰
Angle C = ⁰
Case 1:
Angle B = 48.2 ⁰
c = 17.3
Angle C = 96.8 ⁰
Case 2:
Angle B = ⁰
c = 3.98
Angle C = 13.2 ⁰

5. x = 82.8 ft
x = ft2

6. Exploring Sine, Cosine and Tangent Angle Restrictions
Using your calculator, complete the chart. Round to the nearest thousandth.
1. What do you notice about the sine column? Describe the pattern.
2. What do you notice about the cosine column? Describe the pattern.
3. What do you notice about the tangent column? Describe the pattern.
Angle
sin(angle)
cos(angle)
tan(angle) 30 60 90
120
150
180
210
240
270
300
330
360
Starts at 0 and goes between 1 and -1
undefined
Starts at 1 and goes between -1 and 1
undefined
Sin/Cos = Tan *Tangent is undefined when Cos = 0

7. Remember!!!
a. Angles are measured in
b. We have to check our mode to make sure the calculator knows what measure we are using!!
i. In this class, we will always use , but you should know that radians exist!
 Make sure degree is highlighted
radians and degrees
degrees

8. The Unit Circle
Not in notes- briefly discuss.

9. Not in notes- briefly discuss.

10. Solving Trig Equations
x = 17.46⁰
No solution- sine is always between -1 and 1
x = 41.81⁰

11. Sometimes, there are more than one answer
Sometimes, there are more than one answer. In CCM2, we’re only going to talk about one of them
Not in notes- briefly discuss.

12. Extra Examples – 1st 4 of the HW!
x = 90⁰ or 30 ⁰

13. sine
cosine
tangent
Sin-1
Cos-1
Tan-1

14. You Try:
Solve the equations and express your answer to the nearest tenth degree:
1. sin (x) = cos (x) = tan (x) = -6.7
4. cos (x) = sin (x) = sin(x) = 1.2
No solution
x = 36.9⁰
x = -81.5⁰
x = 150.5⁰
x = 30⁰
x = 17.5⁰

15. Practice at the bottom of pg. 24
Solve the following equations and express your answer to the nearest tenth degree:
sin (x) = 0.8
2) cos (x) = -0.78
3) tan (x) = -9.5
4) sin (x) = 0.366
5) sin (x) =
6) 3tan (x) = -12.8
7) 3sin (x) + 4 = 1.57
8) 4cos (x) – 6 = -5.2
x = -84⁰
x = 53.1⁰
x = 141.3⁰
x = 21.5⁰
x = -50.2⁰
x = -76.8⁰
x = -54.1⁰
x = 78.5⁰

16. An Exploration Work in groups of 3
Raise your hand when you are finished
Notes p. 29
Work as a discovery

17. sin(45) and cos(45) are equal
0.342
0.766
2.747
0.616
0.259
0.466
0.707
0.707 1
sin(45) and cos(45) are equal
tan(45) = 1
0.94
0.866
0.5
They are equal
4. Use your calculator to find the following:
Tan(40) =
Tan(50) =
0.839
1.192
0.839
1.192
What conclusion can you draw about the relationship between the tangent function and sine and cosine?

18. Homework Packet p