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Questions and Answers
What is the value of tan30°/tan60° + cos60°sin30°?
What is the value of tan30°/tan60° + cos60°sin30°?
7/12
Match the angle θ with its corresponding sine, cosine, and tangent values when θ=330°:
Match the angle θ with its corresponding sine, cosine, and tangent values when θ=330°:
sinθ = -1/2 cosθ = √3/2 tanθ = -√3/3
What is the value of tan(π/4)tan(π/3) + cos(π/6)tan(π/6)?
What is the value of tan(π/4)tan(π/3) + cos(π/6)tan(π/6)?
(7√3)/6
If sinθ = 12/13, what is cos(π/2-θ)?
If sinθ = 12/13, what is cos(π/2-θ)?
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What are the possible values of x in the equation 2sinx/2 = √3?
What are the possible values of x in the equation 2sinx/2 = √3?
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What is the period of the function y = cos(2x-π/2) + 2?
What is the period of the function y = cos(2x-π/2) + 2?
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Describe the transformation of the graph of y = cos(2x).
Describe the transformation of the graph of y = cos(2x).
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Is it true that tan(x/2) > -1 implies 0 ≤ x?
Is it true that tan(x/2) > -1 implies 0 ≤ x?
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Study Notes
Trigonometric Values and Identities
- ( \tan(30°)/\tan(60°) + \cos(60°)\sin(30°) ) simplifies to ( 7/12 ).
- For ( \theta = 330° ):
- ( \sin(\theta) = -1/2 )
- ( \cos(\theta) = \sqrt{3}/2 )
- ( \tan(\theta) = -\sqrt{3}/3 ).
Simplifications and Calculations
- ( \tan(\pi/4)\tan(\pi/3) + \cos(\pi/6)\tan(\pi/6) ) calculates to ( (7\sqrt{3})/6 ).
- Given ( \sin(\theta) = 12/13 ), ( \cos(\pi/2 - \theta) ) equals ( 12/13 ).
Solving Equations
- The equation ( 2\sin(x/2) = \sqrt{3} ) has solutions:
- ( x = 2/3\pi )
- ( x = 4/3\pi ).
Graph Analysis
- For the function ( y = \cos(2x - \pi/2) + 2 ):
- The period is ( \pi ).
- The graph represents a translation of ( y = \cos(2x) ) shifted ( \pi/4 ) units along the x-axis and 2 units along the y-axis.
Inequalities
- The inequality ( \tan(x/2) > -1 ) applies for ( 0 \leq x ).
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