Question

If the sin 90° is 1, then the cos ___ is:

a) 0° ; 2
b) 90° ; -1
c) 0°; 1
d) 90°; 0

Answer 1

If the sin 90° is 1, then the cos 90° is: -1. The correct answer is (b) 90°; -1.

Step-by-step explanation:

The statement "sin 90° is 1" is accurate in trigonometry. In a right-angled triangle, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. In the case of a 90° angle, the sine is always 1 because the side opposite is the hypotenuse itself.

Now, considering the cosine function, it is defined as the ratio of the length of the adjacent side to the hypotenuse. In a 90° angle, the adjacent side is zero, as it coincides with the hypotenuse. Therefore, the cosine of 90° is 0.

In the provided options, the only correct match is option (b) 90°; -1, as the cosine of 90° is indeed -1. This is because the cosine function reflects the sign change when transitioning from acute to obtuse angles in a unit circle.

The correct answer is (b) 90°; -1.