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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

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

## SOLUTION This solution is FREE courtesy of BrainMass!

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 =
(c) What is the equation of the circle?
Solution:

Equation of circle will be

3. Given y = 9 sin(8x - π), state the
(a) period

Solution:

Period = 2π/|B| = 2π/8 = π/4

(b) phase shift

Solution:

Phase shift = C/B = π/8

4. Solve the trigonometric equation (sin x)(2cos x − 1) = 0 in the interval [0, 360°).

Solution:

(sin x)(2cos x − 1) = 0
Sinx = 0 or 2cosx-1 =0
Sinx = 0 or cosx = ½

When sinx = 0
x = 0, 180°, 360°

When cosx = ½
x = 60°, 300°

Answer: x = 0°, 60°, 180°, 300°, 360°

(a) Find the exact value of arccos sin( 3π/ 2 )

Solution:
arccos sin( 3π/ 2 ) = arcos(-1) = π

(b) Find the exact value of arcsin sin( 2π/3 )

Solution:

arcsin (sin( 2π/3 )) = 2π/3

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

Solution:

The only solution is x =-1 as given equation is not defined at x = -6.

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

Solution:

cosq =

(b) Find the exact value of sin 2q.

Solution:

sin 2q = 2sinqcosq = 2*

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

Hence proved

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