Find cos(t) where the terminal ray of the angle t radians in standard position passes though the point (-4,-3).

make a sketch of the triangle by drawing a line from (-4,-3) to the x-axis

x = -4 , y = -3, by Pythagoras, r = 5
cos t = x/r = -4/5

okay so if I was suppose to find tan (t)it would be

tan= -3/-4?

or would it be (-3/5)/(-4/5)

same thing

tan t = -3/-4 = 3/4

or

tan t = (-3/5) / (-4/5)
= (-3/5)(5/-4) = 3/4

since tan t = sin t/cos t is an identity you would HAVE to get the same result.

Okay, I feel silly not realizing that the second reduced to 3/4

To find cos(t), we need to determine the x-coordinate of the point where the terminal ray of the angle t radians intersects the unit circle.

In this case, the terminal ray passes through the point (-4, -3). To find the angle t, we need to use the inverse tangent function (tan^(-1)).

The formula for the angle t in radians is t = tan^(-1)(y/x), where (x, y) is the coordinates of the point through which the terminal ray passes.

Let's substitute the given values into the formula:
t = tan^(-1)(-3/-4)
t = tan^(-1)(3/4) [Since -/- = +]

Using a calculator or a trigonometric table, we find that tan^(-1)(3/4) ≈ 0.6435 radians.

Now that we have the value of t, we can find cos(t) by substituting t into the cosine function (cos) or using the Pythagorean identity (sin^2(t) + cos^2(t) = 1).

cos(t) = cos(0.6435) ≈ 0.80399712

Therefore, cos(t) ≈ 0.80399712.