Question

Find (a) sin 0 , (b) cos 0 , and (c) tan 0 for the given quadrantal angle. If the value is undefined, write "undefined." -7π/2

Answer 1

The trigonometric functions for the angle −7π/2 are sin(90°)=1, cos(90°)=0, and tan(90°) is undefined, as it involves division by zero.

Step-by-step explanation:

To find the values of trigonometric functions sin, cos, and tan for the given quadrantal angle of −7π/2, it's important to know that this angle corresponds to an angle measured in the counter-clockwise direction from the positive x-axis.

Firstly, since the full circle is 2π radians, we simplify the angle by finding a coterminal angle within the range of one full circle:

−7π/2 + 4π/2 = −7π/2 + 8π/2 = π/2.

The coterminal angle of π/2 is a 90-degree angle or a quadrantal angle pointing directly upwards along the y-axis. At this position, the coordinates are (0, 1) on the unit circle. Thus, we can determine that:

• sin(π/2) = 1 because sin corresponds to the y-coordinate.
• cos(π/2) = 0 because cos corresponds to the x-coordinate.
• tan(π/2) = sin(π/2)/cos(π/2) which is 1/0, and since division by zero is undefined, tan(π/2) is undefined.