3 Trig Identities Homework PDF

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MAT1275 math problems on trig identities ...

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Session 22: Trigonometric Identities and None-Basic Equations

Exercises 22 In exercises 22.1 – 22.10, prove the given identities. 22.1. cos2 x  tan 2 x 1  cos 2 x

22.2. sin 2 x  cot 2 x 1  sin 2 x

22.3. cot x  cos x

22.4. tan x  sin x

csc x  sin x

22.5. csc x  sin x

cos x tan x

sec x  cos x

22.6. sec x  cos x

sin x cot x

22.7.

tan x tan x  1  cos x 1  cos x

2 csc x

22.8.

22.9.

cot x cot x  1  csc x 1  csc x

2 sec x

22.10.

tan x tan x  1  sec x 1  sec x

2  sec 2 x

22.12.

sin 4 x  cos 4 x sin 2 x

22.11.

cos4 x  sin 4 x cos2 x

cot x cot x  1  sin x 1  sin x

2 sec x

2 csc x

2  csc 2 x

In exercises 22.13 – 22.26, solve the given equations in the interval >0, 2S  . Use radian measure. If it is possible to find exact solutions, write them in terms of S . If it is not possible, round the answers to the nearest thousandth. 2 22.13. cos ( x)

2 22.14. sin ( x)

cos( x)

22.15. sin2 ( x)  sin( x)

22.16. cos2 ( x)  cos( x)

0

22.17. 4 cos 2 ( x)  1 1 22.19. 2 sin 2 ( x)  3sin( x)

sin( x ) 0

22.18. 6 sin 2 ( x)  1 4

2

2

22.20. 2 cos 2 ( x)  7 cos( x)

3

2

22.21. 3sin ( x)  cos( x)  1 0

22.22. 5 cos ( x)  sin( x)  1 0

22.23. 3sin( x)  tan( x)

22.24. cos( x)  tan( x )

22.25. sin( x)  cos( x) 1

3 sin( x)

3 cos( x )

22.26. cos( x )  sin( x ) 1...