Trigonometric Equations

Trigonometric Equations - Problem Solving


If 2cos2x+47cosx=20sin2x, 2 \cos^2{x} + 47 \cos{x} = 20 \sin^2{x} , then what is the value of cosx? \cos{x} ?

In the domain [0,17] [0, 17 ] , how many real solutions are there to cos(πx2)=1 \cos (\pi x^2 ) = -1 ?

Let α\alpha, β\beta and γ\gamma be the period, maximum value and minimum value, respectively, of the function y=sin46x+cos46x.y=\sin^4 6x+\cos^4 6x. What is the value of βπαγ\frac{\beta \pi}{\alpha \gamma}?

List the positive roots of the trigonometric equation cos2xsin22x=0\cos^2 x-\sin^2 2x=0 in ascending order to form a sequence {an}\{a_n\}. What is the value of the constant mm that satisfies k=136ak=mπ?\displaystyle \sum_{k=1}^{36}a_k=m\pi?

What are all possible values of sinθ+8cosθ\sin\theta + 8\cos\theta?


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