Final answer:
After finding the hypotenuse using the Pythagorean theorem, the ratios for sine, cosine, and tangent are approximately 0.753, -0.658, and -1.142 respectively, which do not match the options provided in the question. Thus, none of the answer choices given are correct, and the student should recheck their sources.
Step-by-step explanation:
To find the sine, cosine, and tangent of an angle with a point on the terminal side (-7, 8), we first need to determine the hypotenuse of the right triangle formed by this point and the origin (0, 0). Using the Pythagorean theorem:
hypotenuse = √((-7)^2 + 8^2) = √(49 + 64) = √113
Typically, we then use this hypotenuse to find the sine, cosine, and tangent functions:
- Sine is the opposite side divided by the hypotenuse: sin = 8 / √113
- Cosine is the adjacent side divided by the hypotenuse: cos = -7 / √113
- Tangent is the opposite side divided by the adjacent side: tan = 8 / -7
To simplify, the hypotenuse is approximately √113, which is about 10.63 when rounded. Therefore, the ratios for sine, cosine, and tangent, approximately become:
- Sine: 8 / 10.63 ≈ 0.753
- Cosine: -7 / 10.63 ≈ -0.658
- Tangent: 8 / -7 ≈ -1.142
Looking at the options given in the question, none of them match the actual ratios calculated above. However, if we consider the ratios without calculating the decimal approximation of the hypotenuse, then the ratios can be expressed as:
- Sine: 8 / √113,
- Cosine: -7 / √113,
- Tangent: 8 / -7 or -8/7
None of the answer choices provided are correct as per the calculations. Therefore, we should inform the student of this discrepancy so they can recheck the problem or consult additional resources.