Problem

Problem

Find two angles θ\theta on the unit circle, with 0∘≤θ≤360∘0^\circ \le \theta \le 360^\circ , such that: a. a tan⁡θ=4\tan \theta = 4 b. b cos⁡θ=0.83\cos \theta = 0.83 c. c sin⁡θ=35\sin \theta = \frac{3}{5} d. d cos⁡θ=0\cos \theta = 0 e. e tan⁡θ=6.67\tan \theta = 6.67 f. f cos⁡θ=217\cos \theta = \frac{2}{17}
Intuitive explanation

The key is recognizing that sine and cosine values repeat at predictable intervals on the unit circle. For any trig equation, you're looking for all angles where the point on the circle has a specific coordinate value. Start by finding the reference angle (the acute angle from the nearest axis), then use symmetry to locate all solutions in your given range—typically one in each quadrant where that trig function has the right sign.

Intuitive explanation

The key is recognizing that sine and cosine values repeat at predictable intervals on the unit circle. For any trig equation, you're looking for all angles where the point on the circle has a specific coordinate value. Start by finding the reference angle (the acute angle from the nearest axis), then use symmetry to locate all solutions in your given range—typically one in each quadrant where that trig function has the right sign.

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