Trigonometric Equations

Trigonometric Equations: Level 2 Challenges


Find all values of θ \theta such that

cos2θ=1. \cos^2 \theta = 1.

In the options, nn is an integer.

Given that

cos(A)4sin(A)=1, \cos(A)-4\sin(A)=1,

what are the possible values of

sin(A)+4cos(A)? \sin(A) + 4\cos(A)?

sinθ+cosθ=2sin(90θ),cotθ=?\sin\theta+\cos\theta=\sqrt{2}\sin(90^{\circ}-\theta), \quad \cot\theta = \, ?

Give your answer to the above problem to 3 decimal places.

Find the value of xx between 0 and 180 such that

tan(120x)=sin120sinxcos120cosx.\tan({ 120 }^{ \circ }-x^{ \circ })=\frac { \sin{ 120 }^{ \circ }-\sin x^{ \circ } }{ \cos{ 120 }^{ \circ }-\cos x^{ \circ }}.

If cos4αcos2β+sin4αsin2β=1,\quad \quad \dfrac{\cos^4\alpha}{\cos^2\beta}+\dfrac{\sin^4\alpha}{\sin^2\beta}=1, find the value of sin4βsin2α+cos4βcos2α.\dfrac{\sin^4\beta}{\sin^2\alpha}+\dfrac{\cos^4\beta}{\cos^2\alpha}.


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