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# Trigonometry questions of identity

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1. Express in equivalent form: log x + log 1 - 6 log (y + 4)

2. Points (4, -7) and (6, 3) are endpoints of the diameter of a circle./
(a) What is the exact length of the diameter?
(b) What is the center of the circle?
(c) What is the equation of the circle?

3. Given y = 9 sin(8x - p), state the
(a) period
(b) phase shift

4. Solve the trigonometric equation (sin x)(2cos x − 1) = 0 in the interval [0, 360°).
(a) Find the exact value of arccos sin( 3π/ 2 )
(b) Find the exact value of arcsin sin( 2π/3 )

5. Solve. ( x+13/x+6 ) + ( 84/ x^2-36) = 0

6. Suppose that sin q = 5/13 and that q is a Quadrant II angle.
(a) Find the exact value of cos ϴ
(b) Find the exact value of sin 2ϴ.

7. Prove the identity 1 - (sin x - cos x)2 = sin 2x

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#### Solution Preview

1. Express in equivalent form: log x + log 1 - 6 log (y + 4)
Solution:

Answer:

2. Points (4, -7) and (6, 3) are endpoints of the diameter of a circle.
(a) What is the exact length of the diameter?
Solution:
Diameter

Answer:
(b) What is the center of the circle?
Solution:
Center =
Answer: (5,-2)
(c) What is the equation of the circle?
Solution:
Radius = /2 = ...

#### Solution Summary

This posting includes detailed solutions some questions on solving algebraic equation, solving trigonometric equation and finding equation of circle.

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