Mathematics

Mathematics

Problem

For 0∘<θ<90∘0^\circ<\theta<90^\circ, why is tan⁡θ\tan\theta always greater than sin⁡θ\sin\theta? a) Because cos⁡θ\cos\theta is negative in (0∘,90∘)(0^{\circ},90^{\circ}), dividing sin⁡θ\sin\theta by cos⁡θ\cos\theta enlarges the value b) Because sin⁡θ\sin\theta is always less than cos⁡θ\cos\theta, their ratio exceeds sin⁡θ\sin\theta c) Because cos⁡θ<1\cos\theta<1, dividing sin⁡θ\sin\theta by cos⁡θ\cos\theta increases its value d) Because tan⁡θ=cos⁡θsin⁡θ\tan\theta=\dfrac{\cos\theta}{\sin\theta} and cos⁡θ>sin⁡θ\cos\theta>\sin\theta, so the quotient is larger

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