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Thread: sin question

  1. #1
    Senior Member euclid2's Avatar
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    sin question

    if sino=7/25 what are the other primary trig ratios.
    solve this triangle.
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  2. #2
    Super Member
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    $\displaystyle \sin{\theta} = \frac{y}{r} = \frac{7}{25}$

    y = 7, r = 25. Now we need x to find the other trig ratios. We use Pythagora's theorem:
    $\displaystyle x^2 + y^2 = r^2$

    $\displaystyle x = \pm\sqrt{r^2 - y^2}$

    Which quadrant is this? Take the sign that corresponds for the quadrant. Assume it's Quadrant I, thus

    $\displaystyle x = +\sqrt{625 - 49} = +\sqrt{576} = + 24$

    Now, now you solved the triangle. Simply substitute the values of x, y, and r in other ratios. I recommend that you find sine, cosine, and tangent, then take their reciprocals to get cosecant, secant, and cotangent. Remember:

    $\displaystyle \sin{\theta} = \frac{y}{r}$

    $\displaystyle \cos{\theta} = \frac{x}{r}$

    $\displaystyle \tan{\theta} = \frac{y}{x}$
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