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Hi Katherine, You are to solve for $\theta$ if $8 \cos(\theta)  3 = 1.$ You should first add 3 to each side to get $8 \cos(\theta) = 4$ and then divide by 8 and take the square root to get \[\cos(\theta) = \frac{\pm 1}{\sqrt 2}.\] You should know that $\cos(45^o) = \frac{1}{\sqrt 2}$ so 45 degrees is one solution but how do you find all $\theta$ between 0 and 360 degrees that satisfy the equation? I would use the unit circle with centre at the origin $O.$ If you draw a ray from $O$ at an angle $\theta$ to the positive Xaxis, measured counterclockwise, and it intersects the circle at $P,$ then the Xcoordinate of $P$ is $\cos(\theta)$ and the Ycoordinate of $P$ is $\sin( \theta).$ (I drew a vertical line from $P$ to the Xaxis so that you can use the triangle to see this if you are accustomed to using a right triangle to define the trig functions. Remember that the length of $OP$ is 1.) What other point on the unit circle has the same Xcoordinate? Extend the vertical line from P to intersect the circle at $Q.$ $Q$ has the same xcoordinate as $P$ and using symmetry the measure of the angle from the positive Xcoordinate, clockwise to $OQ$ is $360  \theta$ degrees. Hence $\cos(360  \theta) = \cos(\theta).$ Try this technique with your problem, first starting with $\cos(\theta) = \frac{1}{\sqrt 2}$ and then with $\cos(\theta) = \frac{1}{\sqrt 2}.$ Write back if you need more assistance,  


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