Find the values of the six trigonometric functions of θ with the given constraint. (If an answer is undefined, enter UNDEFINED.)
Function Value = cos θ = 4/5
Constraint = tan θ < 0
Since cosθ > 0 and tanθ < 0, then sinθ < 0
Also: sin²θ = 1 − cos²θ = 1 − 16/25 = 9/25
sinθ = −3/5
cosθ = 4/5
tanθ = sinθ/cosθ = −3/4
cotθ = 1/tanθ = −4/3
secθ = 1/cosθ = 5/4
cscθ = 1/sinθ = −5/3
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Verified answer
Since cosθ > 0 and tanθ < 0, then sinθ < 0
Also: sin²θ = 1 − cos²θ = 1 − 16/25 = 9/25
sinθ = −3/5
cosθ = 4/5
tanθ = sinθ/cosθ = −3/4
cotθ = 1/tanθ = −4/3
secθ = 1/cosθ = 5/4
cscθ = 1/sinθ = −5/3