Use the information given about the angle theta 0 lessthanor

Use the information given about the angle theta, 0 lessthanorequalto theta lessthanorequalto 2 pi, to find the tan theta = -10, sin theta

tan @ = -10

0<= @ <=2 pi it means @ (angle) lies in IV quadrant.

from Sec²@ - tan²@ = 1

Sec@ = +_ ( 1 + tan²@ )^1/2

sec@ = +_ ( 1 +100)^1/2

sec@ = + (101)^1/2

[ +ve sign becasuse in IV quadrant Sec@ is positive)

Cos @ = 1/ Sec@

Cos@ = 1/ (101)^1/2

B) cos 2@ = 2*cos²@ -1

cos 2@ = 2*( 1/(101)^1/2)² -1 = (2/101) - 1

Cos 2@ = - 99/ 101

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c) from Cos 2@ = 1- 2*sin²@

cos@ = 1- 2*sin²(@/2)

sin²(@/2) = (1- cos@)/2 =[ 1- ( 1/(101)^1/2) ] / 2 = 0.4505

sin(@/2)= +_ ( 0.4505)^1/2

sin(@/2) = - 0.671

[ -ve sign because in Iv quadrant sin@ is negative ]

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D) from cos 2@ = 2*cos² @ - 1

cos@ = 2*cos²(@/2) - 1

cos²(@/2) = (cos @+1)/2 = [( 1/ (101)^1/2) +1] / 2 = 0.5495

cos (@/2) = +_ (0.5495)^1/2

cos (@/2) = + 0.741

[ in IV quadrant cos @ = positive]