Question

The segment joing C and D (-0.6, -0.8) is the tangent to the unit circle at D. what is the exact value of...

1. sin(t - 2pi)

2. tan(t + pi)

3. tan(t - 2pi)​

Answer 1

Tan(t+pi) = 3

Explanation:

First let's find the slope of the line through the points and

Note: is the first point . So this means that x%5B1%5D=-2 and y%5B1%5D=0.

Also, is the second point . So this means that x%5B2%5D=0 and y%5B2%5D=3.

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.

m=%283-0%29%2F%280--2%29 Plug in y%5B2%5D=3, y%5B1%5D=0, x%5B2%5D=0, and x%5B1%5D=-2

m=%283%29%2F%280--2%29 Subtract 0 from 3 to get 3

m=%283%29%2F%282%29 Subtract -2 from 0 to get 2

So the slope of the line that goes through the points and is m=3%2F2

Now let's use the point slope formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula

y-0=%283%2F2%29%28x--2%29 Plug in m=3%2F2, x%5B1%5D=-2, and y%5B1%5D=0

y-0=%283%2F2%29%28x%2B2%29 Rewrite x--2 as x%2B2

y-0=%283%2F2%29x%2B%283%2F2%29%282%29 Distribute

y-0=%283%2F2%29x%2B3 Multiply

y=%283%2F2%29x%2B3 Simplify

So the equation that goes through the points and is y=%283%2F2%29x%2B3

Notice how the graph of y=%283%2F2%29x%2B3 goes through the points and . So this visually verifies our answer.

Graph of y=%283%2F2%29x%2B3 through the points and