Let (3, -2) be a point on the Terminal Side of θ. Find the exact values of Cosθ, Secθ, and Cotθ

Answer 1

The point (3, - 2) is in quadrant 4. We must draw a right triangle. When drawing the triangle, draw the hypotenuse from the origin to the point, then draw from the point, vertically to the x-axis. The triangle is always drawn to the x-axis, not the y-axis.

We now have a right triangle with the leg along the x-axis equaling 3 and the leg parallel to the y-axis equaling -2.

Find the hypotenuse using Pythagorean Theorem.

(3)² + (-2)² = c²

c² = 9+4

c = √13

Theta is drawn inside the triangle between the hypotenuse adnd the -axis.

The opp side = -2

The adj side = 3

The hyp = √13

cosθ = adj/hyp = 3/√13, but we can't leave a radical in the denominator so we rationalize:

3/√13 * √13/√13 = (3√13)/13

Therefore cosθ = (3√13)/13 FINAL ANSWER

secθ = 1/cosθ when doing this I like to look at our answer for cosine before we rationalized.

secθ = 1/(3/√13) = √13 / 3 FINAL ANSWER

cotθ = adj/opp = -2/3 FINAL ANSWER

Hope this helps!