Find exact values of the six trigonometric functions for each ...

Question

Find exact values of the six trigonometric functions for each angle A.

Accepted Answer

Welcome back everyone. In this problem, we have a right triangle for which we want to find the values of the six trigonometric functions. For angle N indicated on the diagram, we want to provide exact values and simplify our answers. For our right triangle, its base is 70 units, its height is 24 units and its hypotenuse is units. Now, if we want to figure out the six trigonometric functions, let's just first make a note of what those are. So for every right triangle, the sign of that anger. In this case, Anger N would be equal to the ratio of the opposite side two. The hypotenuse for the cosine of N, it would be equal to the adjacent side two, the hypotenuse that is its ratio and the tangent of our angle would be equal to the ratio of the opposite side to the adjacent side. Likewise, each of these functions have a reciprocal function. So the reciprocal of the sine function is the core equant and the core sequent of that function of that anger. In this case, N would have been one divided by the sign of N since it's, it's the reciprocal. Likewise, the reciprocal of the cosine is the second. So the C of N would be one divided by the cosine of N and the reciprocal of the tangent is the core tangent. So what that means is that if we are able to find the sign cosine and tangent of the anger, we just need to reciprocate it to find the core second, the second and the core tangent. So before we continue, the first thing we need to do is to find the opposite adjacent, the opposite and adjacent sides to our angle and label the hypo that will make it easier for us to work. Now, since our angle is N, the opposite side to N is 24 so I'm going to label that as opposite. Let me put it in red just to make sure we're all seeing it. OK. Likewise, the side adjacent to end is the side with 70 units. So that would be adjacent. And the hypotenuse is the side with 74 units, the side that's opposite to the right angle. Now, we have our opposite, adjacent and hypotenuse labeled, we can go ahead and find those ratios. That means the sign of N would be equal to the opposite side 24 divided by the hypotenuse which is 74. Notice both sides have a common factor of two. So if we factored out two, we will get 12 divided by 37 that would be the sign of N, likewise, the core sign of N would be the adjacent side that is 70 divided by the hypos, which is 74. Again, we have a common factor of two. So when we factor 02, from both, we'll get 35 divided by 37. And that would be the core sign of N. Finally, for the tangent of N, it equals the opposite side which is 24 to the adjacent side, which is 70 both 24 and 70 have a common factor of two. So when we factor of two, then we'll find that it's 12 divided by 35. So that would be the tangent of N. So we have our first three functions. No, we can find the reciprocals. Since the, is the reciprocal of sign, then that means the core sequent of N would be equal to 37 divided by 12. The count of N would be equal to divided by 35. And the cotangent of N would be equal to divided by 12. Therefore, these are the six trigonometric functions for or triangle. Thanks a lot for watching everyone. I hope this video helped.

Find exact values of the six trigonometric functions for each angle A.

Key Concepts

Definition of the Six Trigonometric Functions

Unit Circle and Angle Measurement

Reference Angles and Quadrant Sign Rules

Watch next