Question

Find the trigonometric function value of the corresponding complementary angle. Given that cos 55° 0.5736, find sin 35° sin 35° ~ (Type an integer or decimal rounded to four decimal places as needed.)

Answer 1

The complementary angle to 35 degrees is 90 - 35 = 55 degrees.

Since the cosine of 55 degrees is given as 0.5736, we can use the identity:

cos^2(x) + sin^2(x) = 1

to find the sine of 55 degrees:

sin^2(55) = 1 - cos^2(55)
sin^2(55) = 1 - 0.5736^2
sin^2(55) ≈ 0.6721
sin(55) ≈ 0.8192

Therefore, the sine of the complementary angle, 35 degrees, is equal to the cosine of 55 degrees:

sin(35) = cos(55) ≈ 0.5736

Rounding this to four decimal places, we get:

sin(35) ≈ 0.5736