Question

Find sin(20) when given the following: sin(θ) = 3/5, 0 < θ < π/2.

a. sin(20) = 0.36
b. sin(20) = 0.6
c. sin(20) = 0.8
d. sin(20) = 0.4

Answer 1

To find sin(20), we can use the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b). Substitute the given values and solve to find sin(20) = √3/5.

Step-by-step explanation:

To find sin(20), we can use the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b). In this case, let's take a = 10° and b = 10°, so that 20° = 10° + 10°. We are given that sin(θ) = 3/5, and since θ is in the first quadrant (0 < θ < π/2), we know that sin(θ) is positive. Therefore, sin(10°) = 3/5.

Using the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b), we have sin(20°) = sin(10°)cos(10°) + cos(10°)sin(10°) = (3/5)(√3/2) + (√3/2)(3/5) = 3√3/10 + 3√3/10 = 6√3/10 = √3/5.

So, sin(20) = √3/5.