Question

Find the values of the trigonometric functions of t from the given information.
sec t=3, terminal point of t is in quadrant IV--cos, tan, csc, cot, sin

Answer 1

In quadrant IV, both the x and y values are negative. Further, from right triangle trigonometry, we can determine the cosine from the secant. All you have to do is flip over the secant to get your cosine. Now, in order to find the last side length, you'll have to use the Pythagorean Theorem. c^2=a^2+b^2
Cosine is the adjacent side divided by the hypotenuse (c), so cosine t=1/3. 3^2=x^2+1^2 -> x=sqaure root of 8 = 2*sqrt{2}
So you now should have all three sides. The adjacent is 1, the opposite is 2*sqrt(2), and the hypotenuse is 3. Below I will show the relationships of the side lengths to the trig functions you want. All you gotta do is plug and chug from here!

sine=opposite/hypotenuse cosine=adjacent/hypotenuse
tangent=opposite/ajdacent cotangent=adjacent/opposite
secant=hypotenuse/adjacent cosecant=hypotenuse/opposite

If you have any trouble, let me know