Question

Sin(pi -30°) + cos(3pi/2 + 30°)

Answer 1

$sin(\pi -30)+cos(\frac{3\pi }{2} +30)=sin30+sin30=0.5+0.5=1$

Answer 2

To calculate the value of the expression, let's first evaluate the trigonometric functions:

1. sin(pi - 30°): We know that sin(pi - x) = sin(x). So, sin(pi - 30°) = sin(30°).

2. cos(3pi/2 + 30°): We know that cos(3pi/2 + x) = -sin(x). So, cos(3pi/2 + 30°) = -sin(30°).

Now, we can use the trigonometric values for 30° to calculate the result:

sin(30°) = 1/2 (since it's a common trigonometric value) cos(30°) = √3/2 (also a common trigonometric value)

Now, let's evaluate the expression:

sin(pi - 30°) + cos(3pi/2 + 30°) = sin(30°) + (-sin(30°)) = 1/2 - 1/2 = 0

So, the final result is 0.