If cos A= -6/7, in quadrant 2, determine the exact value of tan 2A
I don't understand how to do this?
To find the exact value of tan 2A, we need to use trigonometric identities. Here's the step-by-step process:
1. Start by drawing a right triangle in quadrant 2, where cos A = -6/7.
- In quadrant 2, the x-coordinate (adjacent side) is negative, and the y-coordinate (opposite side) is positive.
2. Use the Pythagorean theorem to find the length of the hypotenuse.
- In this case, the hypotenuse is the square root of ((-6/7)^2 + 1^2).
3. Now, we need to find sin A. Since cos A = -6/7, we can use the Pythagorean identity sin^2 A + cos^2 A = 1.
- Rearranging the equation, sin^2 A = 1 - (-6/7)^2.
- Find the value of sin A by taking the square root of the result.
4. Now we can find the value of tan A by dividing sin A by cos A.
5. Next, use the double-angle formula for tangent to find tan 2A.
- tan 2A = (2 * tan A) / (1 - tan^2 A)
By following these steps, you should be able to find the exact value of tan 2A.