if sino=7/25 what are the other primary trig ratios.

solve this triangle.

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- Aug 2nd 2008, 06:51 AM #1

- Aug 2nd 2008, 07:10 AM #2

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- Jun 2008
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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:

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

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

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