Concept Check Find a solution for each equation. sec(2θ + 6°) ...

Question

Concept Check Find a solution for each equation. sec(2θ + 6°) cos(5θ + 3°) = 1

Accepted Answer

Welcome back. Everyone. In this problem, we want to determine the value of beta for the equation. The second count of eight beta plus 49 degrees multiplied by the cosine of 17 beta plus 13 degrees equals one. For our answer choices A is nine degrees. B is four degrees C is six degrees and the D is seven degrees. Now, what do we know here? Well, we're dealing with the, and the C and the cosine are very closely related. As a matter of fact, recall that the second of an angle is the reciprocal of the cosine of our angle. So if we are solving this equation, it would be better to have a common term across the board. So that means we can rewrite our equation as one divided by the cosine of eight beta plus degrees multiplied by the cosine of beta plus 13 degrees equals one. No. To get the cosine out of the denominator, we can multiply by the cosine of eight beta plus degrees. And when we do that, then our equation now becomes the cosine of 17 beta plus 13 degrees equals the cores sign of eight beta plus 49 degrees. Now, since both sides are equal, that means the angles must be equal as well. So this would imply that 17 beta plus degrees equals eight beta plus 49 degrees. That means we can solve for beta. So by grouping like terms on the same side, we can subtract it B from both sides. So it's subtracted from the left hand side and from the right hand side. And when we do that, we'll get 17 beta minus eight beta, which equals nine beta plus equals both of these cancer, which is 49 degrees. If nine beta plus 13 equals 49 then that means nine beta equals 49 minus 13 degrees, which equals 36 degrees. And if nine beta equals 36 degrees, then we can divide both sides by nine to get the value for beta. And that means beta equals 36 divided by nine, which equals four degrees. Therefore, the value of beta is four degrees. And when we look in our answer choices that would have been answer choice. B thanks a lot for watching everyone. I hope this video helped.

Concept Check Find a solution for each equation. sec(2θ + 6°) cos(5θ + 3°) = 1

Key Concepts

Reciprocal Trigonometric Functions

Trigonometric Equation Solving

Angle Sum and Multiple Angle Identities

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