Test: Sine, Cosine and Tangent - SAT MCQ

Sine equals Opposite over Hypotenuse.
Therefore, the sine of the angle is 8/10 = 0.8.

Tangent equals Opposite over Adjacent.
Therefore, the tangent of the angle is 4/3 = 1.33

sin(90°) is the ratio of the opposite side to the hypotenuse in a right-angled triangle, and at 90°, the opposite side is equal to the hypotenuse, so sin(90°) = 1.

tan(A) = sin(A)/cos(A) = (3/5)/(4/5) = 3/4.

tan(α + β) = (tan(α) + tan(β))/(1 - tan(α)tan(β))
= (3/4 + 1/3)/(1 - (3/4)(1/3))
= (3/4 + 1/3)/(1 - 1/4)
= (13/12)/(3/4)
=(13/12)/(9/12)
= 13/9.

Cosine equals Adjacent over Hypotenuse.
Therefore, the cosine of the angle is 7/10 = 0.7.

cos(A) = adjacent/hypotenuse
= 8/10
= 4/5

Sine equals Opposite over Hypotenuse.
To find the opposite side, we can use the Pythagorean theorem: √(13² - 5²) = 12.
Therefore, the sine of the angle is 12/13 = 0.92.

Tangent equals Opposite over Adjacent.
Therefore, the tangent of the angle is 3/4 = 0.75.

In a 45°-45°-90° triangle, the ratio of the side opposite the 45° angle to the length of the hypotenuse is 1/√2.