Trigonometry Lecture Notes, Section 5.1



5.1 Day 1 Fundamental Identities

Big Idea: Identities can be used to simplify complicated trig equations.

Big Skill: You should be able to use the basic identities in this section to manipulate trigonometric expressions.

Reciprocal Identities:

[pic] [pic] [pic]

Quotient Identities:

[pic] [pic]

Pythagorean Identities:

[pic] [pic] [pic]

Negative-Angle Identities:

[pic] [pic] [pic]

[pic] [pic] [pic]

MATCHING

1. = A. sin2x + cos2x

2. tan x = B. cot x

3. cos(-x) = C. sec2x

4. tan2x + 1 = D.

5. 1 = E. cos x

Use identities to fill in the blanks.

6. If tan Ө = 2.6, then tan (-Ө) = ________ 7. If cos Ө = -.65, then cos (-Ө) = __________

8. If tan Ө = 1.6, then cot Ө = ________ 9. If cos Ө = 0.8 and sin Ө = 0.6, then tan (-Ө) = ___

10. Given [pic]for ( in Q IV, find the values of:

a. sin Ө b. tan Ө c. sec(-Ө)

You try! Given for ( in Q IV, find the values of

a. sec ( b. sin (

p.194 #12-18even, 32, 34, 44-48

5.1 Day 2 Fundamental Identities – Clean up!

Us: Re-write the expression in terms of the sine and cosine functions only and then simplify the expression so no quotients appear

[pic]

You: Re-write the expression in terms of the sine and cosine functions only and then simplify the expression so no quotients appear

[pic]

Us: Re-write the expression in terms of the sine and cosine functions only and then simplify the expression so no quotients appear

[pic]

You: Re-write the expression in terms of the sine and cosine functions only and then simplify the expression so no quotients appear

[pic]

p.195 #39-48 , 60-76even

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