SOLUTION: Suppose theta is an angle in quadrant III with cos(theta)= -7/25. Find the exact value of the following: a) sin( pi/2

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Question 866002: Suppose theta is an angle in quadrant III with cos(theta)= -7/25. Find the exact value of the following:
a) sin( pi/2 - theta)
b) cot( theta + 4pi)
Answer by lwsshak3(11628) (Show Source):
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Suppose theta is an angle in quadrant III with cos(theta)= -7/25. Find the exact value of the following:
a) sin( pi/2 - theta)
b) cot( theta + 4pi)
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Use x for theta:
Identity: sin(a-b)=sina*cosb-cosb*sina
sin(π/2-x)=sin(π/2)*cosx-cos(π/2)*sinx=1*-7/25-0*sinx=-7/25
a)sin( pi/2 - theta)=-7/25
..
tan(theta)=√(7^2+25^2)=√(49+625)=√674
Identity: tan(a+b)=(tana+tanb)/1-tana*tanb
tan(x+4π)=(tanx+tan4π)/(1-tanx*tan4π)=(√674+0)/1-tanx*0=√674
b) cot( theta + 4pi)=1/tan( theta + 4pi)=1/√674=√674/674

SOLUTION: Suppose theta is an angle in quadrant III with cos(theta)= -7/25. Find the exact value of the following: a) sin( pi/2 - theta) b) cot( theta + 4pi)