# 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 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

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

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 =

Equation of circle will be

3. Given y = 9 sin(8x - Ï€), state the

(a) period

Solution:

Period = 2Ï€/|B| = 2Ï€/8 = Ï€/4

Answer: Ï€/4

(b) phase shift

Solution:

Phase shift = C/B = Ï€/8

Answer: Ï€/8

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

Solution:

(sin x)(2cos x âˆ’ 1) = 0

Sinx = 0 or 2cosx-1 =0

Sinx = 0 or cosx = Â½

When sinx = 0

x = 0, 180Â°, 360Â°

When cosx = Â½

x = 60Â°, 300Â°

Answer: x = 0Â°, 60Â°, 180Â°, 300Â°, 360Â°

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

Solution:

arccos sin( 3Ï€/ 2 ) = arcos(-1) = Ï€

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

Solution:

arcsin (sin( 2Ï€/3 )) = 2Ï€/3

Answer: 2Ï€/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.

Answer: x = -1

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*

Answer:

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

Solution:

Hence proved

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