Find the remaining trigonometric ratios of θ if :

Question

cos θ =− 1 /3 𝑎𝑛𝑑 𝜃 𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑡𝑒𝑠 𝑖𝑛 𝑄𝐼𝐼𝐼

Answer 1

The easiest techniques is to make the right triangle in the first quadrant in order to find all the magnitudes of the thermodynamic functions using the Pythagorean theorem and all the side ratios. The signs in the third quadrant are sin, cos, sec, csc are negative and tan, cot are positive.

The easiest triangle to work with if cos is 1/3 is to make x=1, r = 3 and y = sqrt(3²-1²) = 2sqrt(2)

The magnitudes of the trig functions are obtained from sohcahtoa (The inverse functions are just the reciprocals) and then you adjust the sign for the 3rd quadrant.

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