Trig Gateway

Question 1

How do you use the calibrated unit circle to find cos x? Sin x? Tan x?

What if x is negative?

What if x is greater than 2π?

Are these approximations or exact answers?

Answer 1

Regardless of which trignometric function we are working with, we first want to identify the value for x, the distance traveled around the unit circle from (1, 0). If x is positive, this is in the counterclockwise direction. We count off the increments around the calibrated unit circle until we have traveled x units about the circle.

If we are looking for cos x, we want to find the x-coordinate of our location. If we are looking for sin x, we want to find the y-coordinate of our location. If we are looking for tan x, we want to find sin x/cos x at our location.

If x is greater than 2pi, we want to exploit the period of these trigonometric functions and subtract or add 2pi to find a distance that is marked on the calibrated unit circle, then calculate the desired trig value of that distance.

Question 2

What are the derivatives of the following functions?

sin (x)

cos (x)

tan (x)

Answer 2

d/dx (sin x) = cos x

d/dx (cos x) = -sin x

d/dx (tan x) = sec²x

Question 3

What is are the