How do you find the exact values of other 5 trigonometric functions given csc B = -6/5 and cot B > 0?

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How do you find the exact values of other 5 trigonometric functions given csc B = -6/5 and cot B > 0?

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Answer 1 · 2016-12-20T15:20:02

$sin B = - \frac{5}{6}$ $SinB=-5/6$ , $cos B = (\pm \frac{\sqrt{11}}{6})$ $cosB=(+-sqrt(11)/6)$ , $tan B = (\pm 5 \frac{\sqrt{11}}{11})$ $tanB=(+-5(sqrt(11))/11)$ , $cot B = (\pm \frac{\sqrt{11}}{5})$ $CotB=(+-sqrt(11)/5)$ , $sec B = (\pm 6 \frac{\sqrt{11}}{11})$ $SecB=(+-6(sqrt(11))/11)$

Explanation:

B has two possible values, one in Quadrant 3 and one in Quadrant 4, where Cosecant and Sine are both negative. Plot angle B in the two quadrants where CscB is negative, quadrants 3 and 4. .Use the Pythagorean Theorem to find the length of the missing side in the triangle, $\sqrt{11}$ $sqrt(11)$ . Then, for angle B in quadrants 3 and 4 determine the other trig ratios using the definitions.

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How do you find the exact values of other 5 trigonometric functions given csc B = -6/5 and cot B > 0?

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