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Solve Cos(Pi/4-x), Given cos(x)=-1/6 & Pi/2

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1) Simplify the given expression. Compute the exact answer as a fraction, it should not contain sin, cos, or tan.

cos((PI/4)-x), if cos(x)=-1/6 and PI/2 < x < PI

2) Use factoring, the quadratic formula, or identities to solve the given equation. Find the solution in the interval [0, 2*PI).

5 sin^2(x) + 3 sin (x) = 8

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Solution Summary

This problem solution shows work and logic for solving cos(Pi/4-x), given cos(x)=-1/6 & Pi/2<x<Pi. The solution uses trigonometric identities, the Pythagorean theorem, factoring and substitution. A complete explanation is included.

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1) Solving: cos(Pi/4-x), given cos(x)=-1/6 & Pi/2<x<Pi

Use the trigonometric identity:
cos(u-v)=cos(u)*cos(v) + sin(u)*sin(v)
Substitute:
u=Pi/4, v=x, so cos(v)=cos(x)=-1/6, ...

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