00:01
So in this problem, we're being told to use the fact that the tangent of x is equal to 8 over 15 and that the ccan of x is equal to negative 17 over 15 to find the value of all six trick functions.
00:12
Well, it might be helpful to sketch this triangle first, but the key is which quadrant is it in? well, notice that the tangent value is positive and tangent is positive in the first quadrant as well as the third quadrant.
00:26
Now, the ccant value is negative.
00:29
Remember, ccant is the reciprocal of cosine.
00:32
So whenever cosine is negative, secant's negative.
00:36
Well, cosine is negative in both the second and third quadrants.
00:42
So secant will also be.
00:44
So where do these two overlap? they overlap in the third quadrant.
00:48
So this means if we were to draw in this triangle on our coordinate plane, it would be in the third quadrant.
00:53
And here would be our angle for x.
00:55
Now let's go ahead and label it.
00:57
Well, tangent is opposite over adjacent.
00:59
So the opposite side is eight, but no other.
01:01
This it's going down, so that would be negative 8.
01:04
And the adjacent side is 15, but because it's going to the left, it's negative 15.
01:09
Now, for secant, you can find your hypotenuse by doing pythagin theorem, but remember, secant, that's the reciprocal of cosine, so it's the hypotenuse over the adjacent side.
01:19
So our hypotenuse must be 17.
01:21
Perfect...