5-2 Verifying Trigonometric Identities

5-2 Verifying Trigonometric Identities

Verify each identity. 1. (sec2 ? 1) cos 2 = sin2

SOLUTION:

2. sec2 (1 ? cos2 ) = tan2 SOLUTION:

3. sin ? sin cos2 SOLUTION:

= sin3

4. csc ? cos cot = sin SOLUTION:

5. SOLUTION:

= cot4

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5-2 Verifying Trigonometric Identities

5. SOLUTION:

= cot4

6. tan csc2 ? tan = cot SOLUTION:

7.

?

= cot

SOLUTION:

8.

+

= 2 csc

SOLUTION:

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5-2 Verifying Trigonometric Identities

8.

+

= 2 csc

SOLUTION:

9.

+ tan = sec

SOLUTION:

10.

+

= sin + cos

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5-2 Verifying Trigonometric Identities

10.

+

= sin + cos

SOLUTION:

11.

+

= 1

SOLUTION:

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5-2 Verifying Trigonometric Identities

11.

+

= 1

SOLUTION:

12.

+

SOLUTION:

= 2 sec2 sin

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5-2 Verifying Trigonometric Identities

12.

+

SOLUTION:

= 2 sec2 sin

13. (csc ? cot )(csc + cot ) = 1 SOLUTION:

14. cos4 ? sin4 = cos2 ? sin2 SOLUTION:

15.

+

= 2 sec2

SOLUTION:

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5-2 Verifying Trigonometric Identities

15.

+

= 2 sec2

SOLUTION:

16.

+

= 2 sec

SOLUTION:

17. csc4 ? cot4 = 2 cot2 + 1 SOLUTION:

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5-2 Verifying Trigonometric Identities

17. csc4 ? cot4 = 2 cot2 + 1 SOLUTION:

18.

=

SOLUTION:

19. FIREWORKS If a rocket is launched from ground level, the maximum height that it reaches is given by h = , where is the angle between the ground and the initial path of the rocket, v is the rocket's initial speed,

and g is the acceleration due to gravity, 9.8 meters per second squared.

a. Verify that

=

..

b. Suppose a second rocket is fired at an angle of 80 from the ground with an initial speed of 110 meters per second. Find the maximum height of the rocket.

SOLUTION: a.

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