# Trigonometry questions of identity

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.