Module 5: Circular Functions Trigonometry
Module 5 Circular Functions and Trigonometry
What this module is about
This module is about trigonometric equations and proving fundamental identities. The lessons in this module were presented in a very simple way so it will be easy for you to understand solve problems without difficulty. Your knowledge in previous lessons would be of help in the process
What you are expected to learn
This module is designed for you to: 1. state the fundamental identities 2. prove trigonometric identities 3. state and illustrate the sum and cosine formulas of cosine and sine 4. determine the sine and cosine of an angle using the sum and difference formulas. 5. solve simple trigonometric equations
How much do you know
A. Answer the following: 1. Which of the following does not equal to 1 for all A in each domain? a. sin2 A + cos2 A
c.
b. sec2 A - cos2 A d. tan A cot A
sin A sec A
2. Simplify cos2 A sec A csc A
3. If sin ∝ =
12 4 and cos β = , where ∝ and β are both in the first 13 5 quadrant, find the values of cos (∝ + β ).
4. Sec A is equal to a. cos A b. sin A c.
1 cos A
d.
1 . sin A
5. Express
1 − csc B in terms of cos B and Sin A. cot B 1 − sin B a. cos B – sinB b. c. sin B – cos B cos B cos φ . sin φ cot φ
b. tanφ c. –csc φ d. -1
d.
sin B − 1 cos B
6. Simplify a. 1
7. Multiply and simplify ( 1 – cos2 t ) ( 1 + tan2 t ). 8. Express tan B ( sin B + cot B + cos B ) in terms of sec B. 9. Compute sin
5π π π from the function of and . 12 4 6
10. Solve the equation cos A – 2sin A cos A = 0.
2
What you will do
Lesson 1 Fundamental Trigonometric Identities
To be able to simplify trigonometric expressions and solve trigonometric equations, you must be able to know the fundamental trigonometric identities. The Eight Fundamental Identities: A. Reciprocal Relations 1. sec θ =
1 cosθ 1 sin θ 1 tan θ
2. csc θ =
3. cot θ =
B. Quotient Relations 4. tan θ =
sin θ cosθ cosθ sin θ
5. cot θ =
C.
What this module is about
This module is about trigonometric equations and proving fundamental identities. The lessons in this module were presented in a very simple way so it will be easy for you to understand solve problems without difficulty. Your knowledge in previous lessons would be of help in the process
What you are expected to learn
This module is designed for you to: 1. state the fundamental identities 2. prove trigonometric identities 3. state and illustrate the sum and cosine formulas of cosine and sine 4. determine the sine and cosine of an angle using the sum and difference formulas. 5. solve simple trigonometric equations
How much do you know
A. Answer the following: 1. Which of the following does not equal to 1 for all A in each domain? a. sin2 A + cos2 A
c.
b. sec2 A - cos2 A d. tan A cot A
sin A sec A
2. Simplify cos2 A sec A csc A
3. If sin ∝ =
12 4 and cos β = , where ∝ and β are both in the first 13 5 quadrant, find the values of cos (∝ + β ).
4. Sec A is equal to a. cos A b. sin A c.
1 cos A
d.
1 . sin A
5. Express
1 − csc B in terms of cos B and Sin A. cot B 1 − sin B a. cos B – sinB b. c. sin B – cos B cos B cos φ . sin φ cot φ
b. tanφ c. –csc φ d. -1
d.
sin B − 1 cos B
6. Simplify a. 1
7. Multiply and simplify ( 1 – cos2 t ) ( 1 + tan2 t ). 8. Express tan B ( sin B + cot B + cos B ) in terms of sec B. 9. Compute sin
5π π π from the function of and . 12 4 6
10. Solve the equation cos A – 2sin A cos A = 0.
2
What you will do
Lesson 1 Fundamental Trigonometric Identities
To be able to simplify trigonometric expressions and solve trigonometric equations, you must be able to know the fundamental trigonometric identities. The Eight Fundamental Identities: A. Reciprocal Relations 1. sec θ =
1 cosθ 1 sin θ 1 tan θ
2. csc θ =
3. cot θ =
B. Quotient Relations 4. tan θ =
sin θ cosθ cosθ sin θ
5. cot θ =
C.