Question

Consider ∠A such that cos A = 12/13.a) In which quadrant(s) is this angle? Explain.b) If the sine of the angle is negative, in which quadrant is the angle? Explain.c) Sketch a diagram to represent the angle in standard position, given that the condition in part b) is true.d) Find the coordinates of a point on the terminal arm of the angle.e) Write exact expressions for the other two primary trigonometric ratios for the angle.I would really appreciate if someone answers my question :)

Answer 1

Given cos A = 12/13 for an angle A, it is located in the first or fourth quadrant. If sine of A is negative, it is specifically in the fourth quadrant. The point on the terminal arm with this cosine might be (12, -5), which gives us sin A = -5/13 and tan A = -5/12 for the other trigonometric ratios.

Step-by-step explanation:

The cosine of an angle determines its location on the unit circle. Given cos A = 12/13, we can deduce the following:

1. The angle must be in either the first or fourth quadrant since cosine is positive in these quadrants.
2. If the sine of the angle is negative, the angle must be in the fourth quadrant, because that is where sine values are negative.
3. For a sketch, you would draw the angle in standard position (counter-clockwise from the positive x-axis) ending in the fourth quadrant.
4. The coordinates of a point on the terminal arm can be found using the Pythagorean theorem, which in this case will give us a point like (12, -5) for the given cosine value.
5. The other primary trigonometric ratios are sin A = -5/13 (since it's negative in the fourth quadrant) and tan A = -5/12 (since tangent is sine divided by cosine).