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