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Show and briefly explain your steps to find the value of sin t if

you are given cot t = −4/3 and cos t > 0.

User Siva K
by
7.5k points

1 Answer

4 votes

Answer:

Explanation:

To find the value of sin t given cot t = -4/3 and cos t > 0, we can follow these steps:

Step 1: Use the given information to identify the quadrant in which angle t lies. Since cos t > 0 and cot t = -4/3, we can conclude that t lies in the second quadrant. In the second quadrant, the sine function is positive.

Step 2: Recall the relationship between cotangent and sine. We know that cot t = 1/tan t = cos t / sin t.

Step 3: Substitute the given value of cot t into the cotangent-sine relationship: -4/3 = cos t / sin t.

Step 4: Rearrange the equation to isolate sin t: sin t = cos t / (-4/3).

Step 5: Simplify the expression: sin t = -3/4 * cos t.

Step 6: Since we know that cos t > 0, we can substitute cos t = √(1 - sin^2 t) from the Pythagorean identity for cosine.

Step 7: Square both sides of the equation: cos^2 t = 1 - sin^2 t.

Step 8: Substitute the value of cos t from the Pythagorean identity into the equation: (√(1 - sin^2 t))^2 = 1 - sin^2 t.

Step 9: Simplify the equation: 1 - sin^2 t = 1 - sin^2 t.

Step 10: This equation is true for any value of sin t, so we can choose any value for sin t that satisfies the given conditions in the second quadrant. One possible solution is sin t = -3/5.

Therefore, the value of sin t, given cot t = -4/3 and cos t > 0, is sin t = -3/5.

User Micky Balladelli
by
8.6k points

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