Using reference angles, how do you find trig functions of cos115?

Question

Dylan Arnold · Accepted Answer

On the trig unit circle:

cos (115) = cos (90 + 25) = -sin 25 = -0.42 (Calculator)

sin (115) = sin (90 + 25 ) = cos 25 = 0.90 (Calculator)

#tan (115) = -0.90/0.42 = -2.14#

#cot (115) = 1/-2.14 = - 0.47#

#sec (115) = 1/0.42 = -2.38#

#csc (115) = 1/0.90 = 1.11.#

Zoe Austin · Answer

undefined To find the trigonometric functions of $ \cos(115^\circ) $ using reference angles, you need to first identify the reference angle in the appropriate quadrant. Since $ 115^\circ $ lies in the second quadrant, its reference angle is $ 180^\circ - 115^\circ = 65^\circ $.

Next, you need to determine the sign of $ \cos(115^\circ) $ in the second quadrant. In the second quadrant, cosine is negative. Therefore, $ \cos(115^\circ) $ is negative.

Now, you can find the cosine function value using the reference angle $ 65^\circ $. The cosine function is equal to the cosine of the reference angle in magnitude, but negative in sign due to the quadrant. So, $ \cos(115^\circ) = -\cos(65^\circ) $.

You can find the cosine of $ 65^\circ $ using either a calculator or trigonometric tables. Once you find the cosine of $ 65^\circ $, simply negate it to find $ \cos(115^\circ) $.