SOLUTION: evaluate : tan360* +4sin180* +5cos^2 180* find the five remaining trigonometic Exact function values for angle theta, given that sec(theta)= -4 and sin(theta)>0 .

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Question 1012533: evaluate : tan360* +4sin180* +5cos^2 180*

find the five remaining trigonometic Exact function values for angle theta, given that sec(theta)= -4 and sin(theta)>0 .
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
evaluate : tan360* +4sin180* +5cos^2 180*
= 0 + 4*0 + 5*(-1)^2
= 5
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find the five remaining trigonometric Exact function values for angle theta, given that sec(theta)= -4 and sin(theta)>0
sec negative and sin positive --> Q2
-----
cos = 1/sec = -1/4
sin = sqrt(1 - cos^2) = sqrt(15)/4
csc = 4/sqrt(15) = 4sqrt(15)/15
tan = sin/cos = -sqrt(15)
cot = 1/tan = -sqrt(15)/15

Answer by ikleyn(52860)   (Show Source): You can put this solution on YOUR website!
.
I will solve only one:

evaluate : tan360° +4sin180° +5cos^2 180°.


tan(360°) = 0,

sin(180°) = 0,

cos(180°) = -1.

From here  tan360° +4sin180° +5cos^2 180° = 5.


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