Concept Check Work each problem.For what angles θ between 0° and ...

Question

Concept Check Work each problem.For what angles θ between 0° and 360° is cos θ = sin θ true?

Accepted Answer

Welcome back. Everyone in this problem, we want to find the values of theta in the interval, open bracket, zero degrees, 360 degrees closed parentheses for which the co second of theta equals the second of theta. For our answer choices. A says that theta is 45 and 135 degrees. B says it's 225 and 315 degrees. C says it's 45 and 315 degrees. And D says it's 45 and 225 degrees. Now, what do we know here? We're trying to find the values of theta and we have our equation, the cos of theta equals the S of theta. Now, what do we know? Well, recall that the cosecant is the reciprocal of the sin of theta. So we can rewrite the cosecant as one divided by the sin of theta. And the second is the reciprocal of the cosine. So we can rewrite it as one divided by the cosine of theta. Now, if one divided by the sine of theta equals one divided by the cosine of theta, that must mean our denominators are the same. That is the sine of theta must be equal to the cosine of theta. Now, we have two trigonometric values or functions. So we can't solve for theta yet. However, we can simplify when we divide the equation by one of the, one of the trigonometric functions. So let's say that we are dividing our equation di winding our equation by the cosign of theater to simplify no, we're dividing the sine of theta by the cosine of theta which we know equals the tangent of theta. On the left hand side and on the right hand side, we're dividing the cosine of theta by the cosine of theta which equals one. So now our equation becomes the tangent of theta equals one. Now let's think about it. What value gives us one for the tangent? Well, it would have been 45 degrees because the tangent of 45 degrees equals one. But we're not done yet. Remember, we're looking for values in the interval 0 to 360 degrees, not including 360. So let's think, are there any other values for the tangent? Well, let's use the unit circle to help us. OK. So on the unit circle, OK, we know that 45 degrees gives us a tangent of one. But we also know that the tangent is positive in the 1st and 3rd quadrants. So the tangent would also be positive in the third quadrant and to find the value that would also or the anger that would also give us a tangent of one, then we'd add 180 degrees. Ok. And when we add 180 to 45 we get 225 degrees. Therefore, the could be 45 degrees and 225 degrees. When we look back in our answer choices, that would have been answer choice. D thanks a lot for watching everyone. I hope this video helped.

Concept Check Work each problem.For what angles θ between 0° and 360° is cos θ = sin θ true?

Key Concepts

Trigonometric Functions

Unit Circle

Angle Relationships

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