Question

Tan 0 = -2, 0

lies in the Il quadrant

Find the five remaining trigonometric function values

Answer 1

Sin O =
`(2√(5) )/(5)`

Cos O =
`-(√(5) )/(5)`

Cot O =
`-(1)/(2)`

Csc O =
`(√(5) )/(2)`

Sec O =
`-√(5)`

Explanation:

Do you know the definitions of all the trig functions? If not, you need to memorize them. Also, you need to memorize which functions are positive in each quadrant. All functions are positive in quad I, sine and reciprocal are positive in quad II, tan and reciprocal are positive in quad III, and cos and reciprocal are positive in quad IV. OK?

Tan of an angle is opposite side/adjacent side of a right triangle

If the tan O = - 2. let the opp. side = 2 and adjacent side = 1. Then the hypotenuse =
`\sqrt{2^(2) + 1^(2) } = √(4 + 1) = √(5)`

Sine is positve and equals opp/hyp =
`(2)/(√(5) ) = (2√(5) )/(5)`

Cos is negative and equals adj/hyp =
`-(1)/(√(5) ) = -(√(5) )/(5)`

Cot is negative and is the reciprocal of the tan or adj/opp =
`(-1)/(2)`

Csc is positive and is the reciprocal of the sine or hyp/opp =
`(√(5) )/(2)`

Sec is negative and is the reciprocal of the cos or hyp/adj =
`-√(5)`