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Evaluate sin[2 cos(−1(3/5))].

Aniket Singh

9 Months agoGrade

1 Answer

Askiitians Tutor Team

Approved Tutor Answer9 Months ago

To evaluate the expression sin[2 cos(−1(3/5))], we can break it down into steps.

Step 1: Find cos(−1(3/5))

The expression cos(−1(3/5)) gives us the angle whose cosine is 3/5. Let's denote this angle as θ.

Step 2: Use the Pythagorean Identity

To find sin(θ), we can use the Pythagorean identity:

sin²(θ) + cos²(θ) = 1

Since we know cos(θ) = 3/5, we can substitute:

sin²(θ) + (3/5)² = 1

sin²(θ) + 9/25 = 1

sin²(θ) = 1 - 9/25 = 16/25

sin(θ) = ±4/5

Assuming θ is in the range of [0, π], we take sin(θ) = 4/5.

Step 3: Calculate sin[2θ]

Now, we need to find sin(2θ). We can use the double angle formula:

sin(2θ) = 2 sin(θ) cos(θ)

Substituting the values we have:

sin(2θ) = 2 * (4/5) * (3/5)

sin(2θ) = 2 * 12/25 = 24/25

Final Result

The value of sin[2 cos(−1(3/5))] is 24/25.