Final answer:
sin(-60°) equals -√3/2. The other trigonometric functions can similarly be found, with cos(-60°) = 1/2, tan(-60°) = -√3, csc(-60°) = -2/√3, sec(-60°) = 2, and cot(-60°) = -√3/3.
Step-by-step explanation:
To find the exact values of the six trigonometric functions for the angle -60°, we can rely on the knowledge of the unit circle and the symmetry of trigonometric functions. Since -60° is in the fourth quadrant, we know that cosine and secant will be positive, while sine, tangent, cosecant, and cotangent will be negative.
The sine of any angle can be found using the unit circle or trigonometric identities. Specifically, for an angle of 60°, the sine value is √3/2. Therefore, since -60° is the negative of 60°, sin(−60°) = -√3/2.
Here are the values for the six trigonometric functions at -60°:
- sin(−60°) = -√3/2
- cos(−60°) = 1/2
- tan(−60°) = -√3
- csc(−60°) = -2/√3
- sec(−60°) = 2
- cot(−60°) = -√3/3
It's important to note the reciprocal relationships between these functions: csc(-60°) is the reciprocal of sin(-60°), sec(-60°) is the reciprocal of cos(-60°), and cot(-60°) is the reciprocal of tan(-60°).