Question

If (cos(textangle) = -2/5) and (tan(textangle)) is greater than zero, what is the value of (sin(textangle))?

a. (1/5)
b. (2/5)
c. (3/5)
d. (4/5)

Answer 1

The value of sin(textangle) is (√21/5).

Step-by-step explanation:

To find the value of sin(textangle), we can use the Pythagorean identity: sin²(textangle) + cos²(textangle) = 1. Since we know that cos(textangle) = -2/5, we can substitute this value into the equation and solve for sin(textangle).

sin²(textangle) + (-2/5)² = 1

sin²(textangle) + 4/25 = 1

sin²(textangle) = 1 - 4/25 = 21/25

sin(textangle) = ±√(21/25) = ±(√21/5)

Since tangent is positive, sin(textangle) must also be positive. Therefore, the value of sin(textangle) is (√21/5)