Concept Check Find a solution for each equation. sin(4θ + 2°) c...

Question

Concept Check Find a solution for each equation.   sin(4θ + 2°) csc(3θ + 5°) = 1

Accepted Answer

Welcome back everyone. In this problem, we want to determine the value of beta for the equation, the sine of seven beta plus nine degrees multiplied by the co account of two beta plus 39 degrees equals one. For our answer choices A is four degrees. B is eight degrees, C is six degrees and D is negative six degrees. Now, what do we know here? We're dealing with the functions, the sign and the, and what's important to note is that the sign and the are very closely related recall that the cos of an angle is the reciprocal of its sign. So we can use that idea in our expression to have it having the same trigonometric ratio throughout which makes it easier to solve. So that means we can rewrite our equation as the sign of seven beta plus nine degrees multiplied by one divided by the sign of two beta plus degrees. And that all equals one now to make our expression or, or, or equation sorry simpler, then we can multiply both sides by the sine of two beta plus degrees. So if I multiply, I think I can write it right here, two beta plus 39 degrees on the left. And I do the same on the right, because it's an equation. Then no, on the left hand side, both cancel to leave us with a sign of seven beta plus nine degrees. And on the right hand side, we'll have one multiplied by the sign of two beta plus 39 degrees. Now, let's think about it. Both sides, the left hand side and the right hand side are sign functions. So that must mean that the angles would have to be equal. So in that case, that tells us then that seven beta plus nine must be equal to two beta plus 39 in order for both sides to be equal. So now we can solve for beta. First, let's subtract two be from both sides. No seven B seven beta, sorry minus two, beta is five beta plus nine equals two beta minus two beta, which is zero plus 39. That means five beta would have to be 39 minus nine, which is 30. And if five beta is 30 then beta equals 30 divided by five, which equals six degrees. Therefore, beta is six degrees. And when we look back on our answer choices, that would have been answer choice. C Thanks a lot for watching everyone. I hope this video helped.

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Concept Check Find a solution for each equation. sin(4θ + 2°) csc(3θ + 5°) = 1

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