Question

Am I able to evaluate sin(cos^1(7/11)) without a calculator? If yes, how? ...?

Answer 1

Yes, you can evaluate sin(cos^-1(7/11)) without a calculator. The result can be simplified to √(72/121).

Step-by-step explanation:

Yes, you can evaluate sin(cos-1(7/11)) without a calculator. Let's break it down step by step:

1. cos-1(7/11) represents the inverse cosine of 7/11. Inverse cosine is the angle whose cosine is equal to the given value. So, cos-1(7/11) is the angle whose cosine is 7/11.
2. To evaluate sin(cos-1(7/11)), we need to find the sine of the angle we found in the previous step.
3. Since we know that sin2(θ) + cos2(θ) = 1, we can use this relationship to find sin(θ) when we know cos(θ).
4. Let's assume the angle we found in step 1 is θ. We know that cos(θ) = 7/11, so we can substitute this value into the equation sin2(θ) + (7/11)2 = 1 and solve for sin(θ).
5. By solving the equation, we find that sin(θ) = √(1 - (7/11)2).
6. Finally, we can simplify the expression sin(θ) = √(1 - (49/121)) or sin(θ) = √(72/121).

Therefore, sin(cos-1(7/11)) can be evaluated as √(72/121).

Answer 2

If this function is:
sin(cos(7/11))
Then it can not be evaluated without a calculator.