Question

If tan 0= 12/5 and cos 0= -15/3 , then what is sin 0

Answer 1

To find sin 0 given tan 0 and a potentially incorrect cos 0, we use the Pythagorean identity, assuming cos 0 = -3/5 due to value constraints, which gives sin 0 as 4/5.

Step-by-step explanation:

To find sin 0 when given that tan 0 = 12/5 and cos 0 = -15/3, we can use trigonometric identities and the Pythagorean theorem. However, there is an issue with the given value of cosine; since cosine values must be between -1 and 1, and -15/3 is equal to -5, we will assume that the correct value might be -3/5 instead to proceed with the calculation. The Pythagorean identity states that sin^2(0) + cos^2(0) = 1.

Assuming cos 0 = -3/5, to find sin 0:

1. Use the Pythagorean identity to express sin²(0): sin²(0) = 1 - cos²(0).
2. Substitute the value of cos 0: sin²(0) = 1 - (-3/5)² = 1 - 9/25 = 16/25.
3. Take the positive or negative square root of 16/25 to find sin 0. Since tan 0 is positive and cos 0 is negative, 0 must be in the second quadrant where sin is positive. So, sin 0 = 4/5.