value of
sin18degree-sin66degree+sin60 degree
plug in calc to get roughly
0.261496941........
can't use calculator
To find the value of the expression sin(18°) - sin(66°) + sin(60°), we can use the trigonometric identity:
sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
Let's break down the expression:
1. sin(18°) - sin(66°) + sin(60°)
Now, we can use the trigonometric identity above to rewrite the first two terms:
2. (sin(18°)cos(66°) - cos(18°)sin(66°)) + sin(60°)
We need to know the exact values of sin(18°), cos(18°), sin(66°), cos(66°), and sin(60°). One way to determine these values is by using the unit circle or a calculator.
Using a calculator, we can find:
sin(18°) ≈ 0.309
cos(18°) ≈ 0.951
sin(66°) ≈ 0.913
cos(66°) ≈ 0.410
sin(60°) = √3/2 ≈ 0.866
Now, we substitute these values back into equation (2):
(sin(18°)cos(66°) - cos(18°)sin(66°)) + sin(60°)
(0.309 * 0.410) - (0.951 * 0.913) + 0.866
Evaluating the expression, we get:
0.126 - 0.870 + 0.866 ≈ 0.122
Therefore, the value of sin(18°) - sin(66°) + sin(60°) ≈ 0.122.