find the exact value of the remaining trigonometric functions of θ satisfying the given conditions cos θ 4/5 tan θ < 0

Question

Sin θ=

Tanθ=

Cscθ=

Secθ=

Cotθ=

Answer 1

Hi Kai!

Think you're missing an equal sign. Cosθ = 4/5, Tanθ < 0

The only quadrants where Cosθ is + is I and IV. Since

Tanθ < 0, this must place the angle in the 4th quadrant.

Will call the reference angle θ ', where θ ' = 360 - θ

4

-

5

------------------------

\ θ ' |

\ | -3

1 \ | --

\ | 5

Sinθ = opp/hyp = (-3/5) / 1 = -3/5

Tanθ = opp/adj = (-3/5) / (4/5) = -3/4

Cscθ = hyp/opp = 1/(-3/5) = -5/3

Secθ = hyp/adj = 1/(4/5) = 5/4

Cotθ = adj/opp = (4/5)/(-3/5) = -4/3

Answer 2

The cosine is positive and the tangent is negative in the 4th quadrant.

Sin Theta = -3/5 Csc Theta = - 5/3

Cos Theta = 4/5 (given) Sec Theta = 5/4

Tan Theta = - 3/4 Cot Theta = - 4/3