ONE
    Númas
    ← Back to the programme
    NationalEasyTrigonometry10–12

    Cosine and Tangent from a Known Sine

    Cosseno e Tangente a Partir do Seno

    Given that sin⁡α=35\sin \alpha = \dfrac{3}{5} and that α\alpha belongs to the second quadrant, determine cos⁡α\cos \alpha and tan⁡α\tan \alpha.

    The fundamental relation fixes how large cos⁡α\cos \alpha is, but not its sign; the quadrant is what decides the sign.

    Solution

    Step 1 of 3

    1. 1.sin⁡2α+cos⁡2α=1⇒cos⁡2α=1−925=1625\sin^{2} \alpha + \cos^{2} \alpha = 1 \Rightarrow \cos^{2} \alpha = 1 - \dfrac{9}{25} = \dfrac{16}{25}