Find the exact value of the six trigonometric functions of the angle whose terminal side contains point (3,-9)

Question

Need to find

sin

cos

tan

csc

sec

cot

Answer 1

The angle is in quadrant 4 where the cos and the sec are positive and the others are negative.

The magnitude of the function comes from the Pythagorean Theorem.

The magnitude of the tan is 9/3, the magnitude of the sin is 3sqrt(10)/10 and the magnitude of cos is sqrt(10)/10.

You might like to remember the mnemonic "AllSinTanCos" which tells you which functions are positive in quadrant 1,2,3,4.