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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 âˆ’ 1) = 0 in the interval [0, 360Â°).
(a) Find the exact value of arccos sin( 3Ï€/ 2 )
(b) Find the exact value of arcsin sin( 2Ï€/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 Ï´
(b) Find the exact value of sin 2Ï´.

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

https://brainmass.com/math/functional-analysis/trigonometry-questions-identity-612173

#### Solution Preview

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

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

(b) What is the center of the circle?
Solution:
Center =