Question

Find the exact value of each expression involving trigonometric angles.

a.cos40°cos50°−sin40°sin50°
b. sin37°cos7°−cos37°sin7°

Answer 1

To find the exact value of each expression, use the trigonometric identities and angle sum formulas.

Step-by-step explanation:

To find the exact value of each expression, we can use the trigonometric identities and angle sum formulas.

(a) Using the formula for cos(A - B), we have:

cos(40° - 50°) = cos(40°)cos(50°) + sin(40°)sin(50°)

Plugging in the values, we get:

cos(40°)cos(50°) + sin(40°)sin(50°)

= (0.766)(0.643) + (0.643)(0.766)

= 0.493 + 0.493

= 0.986

(b) Applying the same formula, we have:

cos(37° - 7°) = cos(37°)cos(7°) + sin(37°)sin(7°)

Substituting the values, we get:

cos(37°)cos(7°) + sin(37°)sin(7°)

= (0.798)(0.991) + (0.602)(0.133)

= 0.791 + 0.080

= 0.871