use the values of tan O = 2 and sin o < 0 to find the values of all six trig functions

Question

1. use the values of tan O = 2 and sin o < 0 to find the values of all six trig functions

Sin O

cos

csc

sec

tan

cot

1. use the values of sec x = -17/15 and sin x > 0 to find the values of all six trig function

sin x

csc x

cos x

sec x

tan x

cot x

Answer 1

picture: right triangle opposite = 2, adjacent = 1, so hypotenuse must be sqrt(5)

since sine is negative and tangent is positive, then cosine must be negative as well

since tan = sin/cos; this is quadrant 3

tan T = 2

sin T = -(2/5) sqrt(5)

cos T = -sqrt(5)/5

csc T = -sqrt(5)/2

sec T = -sqrt(5)

cot = 1/2

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then cos x = -15/17; since sine is positive and cosine is negative, then tangent is negative

since tan = sin/cos; this is quadrant 2; adjacent = -15 and hypotenuse = 17, so opposite must be 8

sin x = 8/17

cos x = -15/17

tan x = -8/15

csc x = 17/8

sec x = -17/15

cot x = -15/8

Answer 2

When TanΘ = 2 = SinΘ/CosΘ, and SinΘ<0, this can be a -1,-2,√5 triangle in the 3rd quadrant.

SinΘ = -2/√5

CscΘ = -√5/2

CosΘ = -1/√5

SecΘ = -√5

TanΘ = 2

CotΘ = 1/2

use the values of sec x = -17/15 and sin x > 0 to find the values of all six trig function

SinΘ = 8/17

CscΘ = 17/8

CosΘ =-15/17

SecΘ = -17/15

TanΘ = -8/15

CotΘ = -15/8