For an acute angle it is known that

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

For an acute angle θ\theta it is known that sin⁡θ=513\sin\theta = \dfrac{5}{13}. Answer all parts sequentially. (i) Find cos⁡θ\cos\theta. (ii) Determine tan⁡θ\tan\theta. (iii) Evaluate the expression 2sin⁡θ+3cos⁡θ2\sin\theta + 3\cos\theta. (iv) Show that tan⁡2θ+1=1cos⁡2θ\tan^{2}\theta + 1 = \dfrac{1}{\cos^{2}\theta} for the values calculated.

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