If $Sin theta = 5/13$ , theta in quadrant II, how do you find the exact value of each of the remaining trigonometric functions of theta?

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Answer 1 · 2016-08-20T20:46:04

$sin theta = 5/13" "cos theta = -12/13" "tan theta = 5/-12$

$cosec theta = 13/5" "sec theta = 13/-12" "cot theta = -12/5$

$sin theta$ is defined as $("opposite")/("hypotenuse")$ or on a Cartesian grid, $sin theta =y/r$

The sides of the right-angled triangle in this case are $5, 12, 13$

HOwever, in Quadrant ll, the x-values are negative, (-12)

The values of the 6 trig ratios in the second quadrant will be:

$sin theta = 5/13" "cos theta = -12/13" "tan theta = 5/-12$

$cosec theta = 13/5" "sec theta = 13/-12" "cot theta = -12/5$

If Sin theta = 5/13Sin theta = 5/13, theta in quadrant II, how do you find the exact value of each of the remaining trigonometric functions of theta?