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#