can anyone help me with this question.

Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P and the exact values of the trig functions of t, whenever possible.
(a) -pi
(b) 6pi

cos(-pi)=cos(pi)=-1

Note: cos(-x)=cos(x), cos is an even function

cos(6π)=cos(0)=1
Note: cos(x)=cos(x-2kπ) where k is an integer.

sin(x) = sqrt(1-cos²(x))
tan(x) = sin(x)/cos(x)

To find the coordinates of a point on the unit circle U that corresponds to a given angle t, you can use the following formulas:

x = cos(t)
y = sin(t)

Let's solve the problem step by step:

(a) For t = -π:
Plug in the value of t into the formulas to find the coordinates of P:

x = cos(-π) = -1
y = sin(-π) = 0

So the coordinates of P are (-1, 0).

To find the exact values of the trigonometric functions, we can use the reference angle principle. The reference angle is the positive acute angle formed between the terminal side of the angle and the x-axis.

Since t = -π, its reference angle is π.

We can now find the trigonometric functions:

cos(t) = cos(-π) = cos(π) = -1 (The cosine function is symmetrical about the y-axis.)
sin(t) = sin(-π) = sin(π) = 0 (The sine function is symmetrical about the origin.)
tan(t) = sin(t)/cos(t) = 0/-1 = 0 (tan is undefined when cos(t) = 0)

(b) For t = 6π:
Plug in the value of t into the formulas to find the coordinates of P:

x = cos(6π) = 1
y = sin(6π) = 0

So the coordinates of P are (1, 0).

To find the exact values of the trigonometric functions, we again consider the reference angle. Since t = 6π, its reference angle is 0, as it lies on the positive x-axis.

We can now find the trigonometric functions:

cos(t) = cos(6π) = cos(0) = 1 (The cosine function is periodic with a period of 2π.)
sin(t) = sin(6π) = sin(0) = 0 (The sine function is periodic with a period of 2π.)
tan(t) = sin(t)/cos(t) = 0/1 = 0