00:01
So we have negative pi over 2 less than or equal to theta less than or equal to pi over 2.
00:10
And we want to find theta so that 5 times the tangent squared of theta is equal to negative 5 times the squared of 3 times the tangent of theta.
00:27
Well, that means then that we can have the tangent of theta is equal to zero, or the tangent of theta is equal to negative 5 squared of 3 divided by 5.
00:48
And i got that by, well, if a tangent of theta is zero, then both sides of the equation are are zero, so that's true.
01:00
And then if tangent of theta is not zero, i can divide both sides by the tangent of theta.
01:07
And i get then five tangent of theta is negative five square root of three.
01:14
So that means then that tangent of theta is negative five square root of three divided by five, which is negative square root of three.
01:24
And this is equal to negative square root of 3 over 2 divided by 1 half so that means that the sine of theta is positive or negative square root of 3 over 2 and the cosine of theta is positive or negative 1 half and it must be in quadrant 2 or quadrant 4, because that is where the tangent is negative...