You found trigonometric values using the unit circle. (Lesson 4-3)
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2 You found trigonometric values using the unit circle. (Lesson 4-3) LEQ: How do we identify and use basic trigonometric identities to find trigonometric values & use basic trigonometric identities to simplify and rewrite trigonometric expressions?
3 identity trigonometric identity cofunction odd-even identities
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5 Use Reciprocal and Quotient Identities A. If, find sec θ. Reciprocal Identity Divide. Answer:
6 Use Reciprocal and Quotient Identities A. If, find sec θ. Reciprocal Identity Divide. Answer:
7 Use Reciprocal and Quotient Identities B. If and, find sin x. Reciprocal Identity Quotient Identity Substitute for cos x.
8 Use Reciprocal and Quotient Identities Divide. Multiply each side by. Simplify. Answer:
9 Use Reciprocal and Quotient Identities Divide. Multiply each side by. Simplify. Answer:
10 If, find sin. A. B. C. D.
11 If, find sin. A. B. C. D.
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13 Use Pythagorean Identities If cot θ = 2 and cos θ < 0, find sin θ and cos θ. Use the Pythagorean Identity that involves cot θ. cot 2 θ + 1 = csc 2 θ (2) = csc 2 θ cot θ = 2 5 = csc 2 θ Simplify. Pythagorean Identity = csc θ Take the square root of each side. Reciprocal Identity Solve for sin θ.
14 Use Pythagorean Identities Since is positive and cos θ < 0, sin θ must be negative. So. You can then use this quotient identity again to find cos θ. Quotient Identity cot θ = 2 and Multiply each side by.
15 Use Pythagorean Identities So, Answer:
16 Use Pythagorean Identities So, Answer: Check sin 2 θ + cos 2 θ = 1 Pythagorean Identity Simplify.
17 Find the value of csc and cot if cos < 0. and A. B. C. D.
18 Find the value of csc and cot if cos < 0. and A. B. C. D.
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20
21 If cos x = 0.75, find Use Cofunction and Odd-Even Identities Factor. Odd-Even Identity Cofunction Identity cos x = 0.75 Simplify.
22 So, = Use Cofunction and Odd-Even Identities Answer:
23 So, = Use Cofunction and Odd-Even Identities Answer: 0.75
24 If cos x = 0.73, find. A B C D. 0.73
25 If cos x = 0.73, find. A B C D. 0.73
26 Solve Algebraically Simplify by Rewriting Using Only Sine and Cosine Simplify. Pythagorean Identity Multiply. Simplify. So, = cos x.
27 Simplify by Rewriting Using Only Sine and Cosine Support Graphically The graphs of appear to be identical. and y = cos x Answer:
28 Simplify by Rewriting Using Only Sine and Cosine Support Graphically The graphs of appear to be identical. and y = cos x Answer: cos x
29 Simplify csc x cos x cot x. A. cot x B. tan x C. cos x D. sin x
30 Simplify csc x cos x cot x. A. cot x B. tan x C. cos x D. sin x
31 Simplify by Factoring Simplify cos x tan x sin x cos 2 x. Solve Algebraically cos x tan x sin x cos 2 x = sin 3 x Original expression Quotient Identity Multiply. Factor. So, cos x tan x sin x cos 2 x = sin 3 x. Pythagorean Identity Simplify.
32 Support Graphically Simplify by Factoring The graphs below appear to be identical. Answer:
33 Support Graphically Simplify by Factoring The graphs below appear to be identical. Answer: sin 3 x
34 Simplify cos 2 x sin x cos(90 x). A. sin 3 x B. sin 3 x C. cos 2 x 1 D. sin x cos x
35 Simplify cos 2 x sin x cos(90 x). A. sin 3 x B. sin 3 x C. cos 2 x 1 D. sin x cos x
36 Simplify by Combining Fractions Simplify. Common denominator Multiply. Add the numerators. Simplify. Pythagorean Identity
37 Simplify by Combining Fractions Reciprocal Identity Reciprocal and Quotient Identities Divide out common factor. 2csc 2 x. Reciprocal Identity Answer:
38 Simplify by Combining Fractions Reciprocal Identity Reciprocal and Quotient Identities Divide out common factor. 2csc 2 x. Reciprocal Identity Answer: 2 sec 2 x 2 sec 2 x
39 Simplify. A. cos x B cos x C. 2 sin x D. 2 csc x
40 Simplify. A. cos x B cos x C. 2 sin x D. 2 csc x
41 Rewrite to Eliminate Fractions Rewrite as an expression that does not involve a fraction. Pythagorean Identity Reciprocal Identity Reciprocal Identity Quotient Identity
42 So, = tan 2 x. Rewrite to Eliminate Fractions Answer:
43 So, = tan 2 x. Rewrite to Eliminate Fractions Answer: tan 2 x
44 Rewrite as an expression that does not involve a fraction. A. 2 tan 2 x B. 1+ sin x C. 1 cos x D. 2 sin x
45 Rewrite as an expression that does not involve a fraction. A. 2 tan 2 x B. 1+ sin x C. 1 cos x D. 2 sin x
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