Download Unit 5A.3

Secondary Math 3
Unit 5A.1 – Trig Functions and Solving Right Triangles
Objectives:


Know the 6 trigonometric functions
Solve right triangles using the 6 trigonometric functions
Notes:
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Secondary Math 3
Assignment 5A.1
Find the value of each trigonometric ratio.
1. tan 𝑍
2. cos 𝐶
3. sin 𝐶
Find the values of the six trigonometric functions for angle 𝜽.
5.
6.
7.
8.
9.
10.
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4. tan 𝑋
Secondary Math 3
Assignment 5A.1 cont
In a right triangle, ∠𝑨 𝒂𝒏𝒅 ∠𝑩 are acute.Find the values of the five remaining trigonometric functions.
8
3
11. tan 𝐴 = 15
12. cos 𝐴 = 10
13. tan 𝐵 = 3
14. sin 𝐵 =
4
9
Use a trigonometric function to find each value of x. Round to the nearest tenth.
16.
17.
19.
20.
18.
21.
22. Devon wants to build a rope bridge between his treehouse and Cheng’s treehouse. Suppose Devon’s
treehouse is directly behind Cheng’s treehouse. At a distance of 20 meters to the left of Devon’s
treehouse, an angle of 52° is measured between the two treehouse. Find the length of the rope.
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Secondary Math 3
Unit 5A.2 – Special Right Triangle Ratios
Objectives:

Solve special right triangles.
Notes:
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Secondary Math 3
Assignment 5A.2
Find the exact value of each trigonometric function.
1. tan 60°
2. sin 60°
3. cos 45°
4. sec 30°
5. cot 60°
6. csc 30°
7. cos 30°
8. sin 30°
9. tan 30°
10. csc 45°
11. cot 45°
12. sec 60°
13. sin 45°
14. cos 60°
15. tan 45°
16. cot 30°
17.
18.
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Secondary Math 3
Assignment 5A.2 (cont.)
19. A boy flying a kite lets out 300 feet of string which makes an angle of 30° with the ground. Assuming
that the string is straight, how high above the ground is the kite?
20. A ladder leaning against the wall makes an angle of 60° with the ground. If the foot of the ladder is
6.5 feet from the wall, how high on the wall is the ladder?
21. An airplane climbs at an angle of 30° with the ground. Find the ground distance it has traveled
when it has attained an altitude of 400 feet.
22. A wire attached to the top of a pole reaches a stake in the ground 20 feet from the foot of the pole
and makes an angle of 60° with the ground. Find the length of the wire.
23. In a 30° − 60° − 90° triangle, the longer leg has a length of 5. What is the length of the shorter leg?
a.
5√3
3
b.
5√3
2
c.
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10√3
3
d. 5√3
Secondary Math 3
Unit 5A.3 – Define General Angles and Use Radian Measure
Objectives:





Students will be able to draw angles in standard position.
Students will understand coterminal angles.
Students will understand what a radian is.
Students will be able to convert between degrees and radians.
Students will be able to find the arc length and area of a sector.
Notes:
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Secondary Math 3
Assignment 5A.3
Draw an angle with the given measure in standard position. Find one positive and one negative angle
that are coterminal with the given angle.
1. 75°
2. 160°
3. -90°
4. -120
5. 295°
6. A lid on a jar rotates
420° before coming off.
Rewrite each degree measure in radians and each radian measure in degrees.
7. 330°
8.
5𝜋
6
9. − 3
𝜋
10. -50°
11. 40°
12. 5𝜋
Find the arc length and area of a sector with the given radius r and central angle 𝜽.
13. 𝑟 = 4 𝑖𝑛. , 𝜃 =
𝜋
6
14. 𝑟 = 3 𝑚, 𝜃 =
5𝜋
12
Fill in the blank.
360° = _______Radians
16.
17.
18.
19.
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15. 𝑟 = 15𝑐𝑚, 𝜃 = 45°
Secondary Math 3
Unit 5A.4 – Trigonometric Functions and General Angles
Objectives:




Students will understand trigonometric functions for general angles.
Students will be able to connect special right triangles to the unit circle in Q1.
Students will be able to expand the unit circle to all quadrants.
Students will understand reference angles.
Notes:
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Secondary Math 3
(5A.4 Notes Continued)
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Secondary Math 3
Task 5A.4: Filling in the Unit Circle
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Secondary Math 3
(Task 5A.4 continued)
UNIT CIRCLE
Use the values from the previous page to display the radian measures that are equal to the given
degree measures. Write the equivalent radian measure beside the given degree measure.
Fill in the values.
Trigonometric Values for Special Triangles
Tangent
Cosecant
Secant
tan 30°=
csc 30°=
sec 30°=
Sine
sin 30°=
Cosine
cos 30°=
sin 45°=
cos 45°=
tan 45°=
csc 45°=
sec 45°=
cot 45°=
sin 60°=
cos 60°=
tan 60°=
csc 60°=
sec 60°=
cot 60°=
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Cotangent
cot 30°=
Secondary Math 3
Assignment 5A.4
The terminal side of 𝜽 in standard position contains each point. Find the exact values of the six
trigonometric functions of 𝜽.
1. (-6, 8)
2. (3, 0)
3. (4, -2)
Sketch each angle. Then find its reference angle.
4. 195°
5. 285°
7𝜋
4
8. − 4
7.
6. -250°
𝜋
9. 400°
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.
4
5
10. sin 𝜃 = ; Quadrant II
11. cos 𝜃 = −
8
;
17
Quadrant III
2
3
12. tan 𝜃 = − ; Quadrant IV
Evaluate the trigonometric function given. (Hint: draw the reference angle.)
13. sin
5𝜋
6
16. sin 90
14. cos
4𝜋
3
15. tan
17. cos 𝜋
7𝜋
4
18. tan 270
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Secondary Math 3
Unit 5A.5 – Inverse Trigonometric Functions
Objectives:

Students will be able to relate the concept of inverse functions to trigonometric
functions
Notes:
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Secondary Math 3
Assignment 5A.5:
Find the exact value without using a calculator.
1
√3
2
2. sin−1 − 2
3. cos−1 2
1
4. tan−1 1
5. tan−1 −1
6. cos−1 0
7. tan−1 0
8. sin−1 1
1. sin−1
Use a calculator to find the approximate value. Put your answer in degrees.
9. sin−1(0.362)
11. tan−1 (−12.5)
10. sin−1(0.67)
12. cos−1(−0.23)
Use a calculator to find the approximate value. Express your answer in radians.
13. tan−1 (2.37)
15. sin−1(−0.46)
14. tan−1 (22.8)
16. cos−1(−0.853)
Find the exact value without a calculator.
1
18. sin(tan−1 1)
17. cos (sin−1 (2))
𝜋
1
2
19. sin−1(cos( 4 ))
20. cos (2 sin−1 ( ))
21. cos(tan−1 √3)
22. tan−1 (cos 𝜋)
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Secondary Math 3
Find an algebraic expression equivalent to the given expression. (HINT: form a right triangle)
23. sin(tan−1 𝑥)
24. tan(sin−1 𝑥)
25. A boat is traveling west to cross a river that is 190 meters wide. Because of the current, the boat
lands at point X, which is 59 meters from its original destination point P. Write an inverse
trigonometric function that can be used to find 𝜃, The angle at which the boat veered south of
the horizontal line. Then find the measure of the angle to the nearest tenth.
26. A 24-foot tree is leaning 2.5 feet left of vertical, as shown in the figure. Write an inverse
trigonometric function that can be used to find 𝜃, the angle at which the tree is leaning. Then
find the measure of the angle to the nearest degree.
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