What are the values of sin(-t), cos(-t), and tan(-t)?

The values of trigonometric functions for negative angles can be determined using the properties of odd and even functions. The sine function is odd, which means that sin(-t) equals -sin(t). This is consistent for all values of t, as the graph of the sine function is symmetric with respect to the origin.

The cosine function, in contrast, is an even function. This means that cos(-t) is equal to cos(t). The cosine graph is symmetric about the y-axis, which reinforces this property.

The tangent function, which is the ratio of sine and cosine (tan(t) = sin(t)/cos(t)), is an odd function as well. Therefore, tan(-t) is equal to -tan(t) because both sine and cosine values will affect the sign appropriately.

Combining these properties related to odd and even functions gives us the final values:

• sin(-t) = -sin(t)

• cos(-t) = cos(t)

• tan(-t) = -tan(t)

This matches the answer choice that states:

• For sin(-t), you obtain -sin(t).

• For cos(-t), you find it equals cos(t).

• For tan(-t), the value becomes -tan(t