Thread: Trig functions

1. Trig functions

1) Find the exact measures of sin2x, cos2x, and tan2x using the double angle formulas, that sinx = -12/13. Show all work.

2) Find the exact value of the trig function given that sinx = 12/13 and cosy = -4/5 and you are in Quadrant 2. Show all work.

3) Find all solutions of the equation cosx + sin2x = 0 in the interval [0, 2π). For this one, I changed sin2x to 2sinxcosx, then factored out a cosx, for it to be cosx(1 + 2sinx), but am unsure where to go from there.

Any help is appreciated!
Thanks.

2. Originally Posted by live_laugh_luv27
1) Find the exact measures of sin2x, cos2x, and tan2x using the double angle formulas, that sinx = -12/13. Show all work.

2) Find the exact value of the trig function given that sinx = 12/13 and cosy = -4/5 and you are in Quadrant 2. Show all work.

3) Find all solutions of the equation cosx + sin2x = 0 in the interval [0, 2π). For this one, I changed sin2x to 2sinxcosx, then factored out a cosx, for it to be cosx(1 + 2sinx), but am unsure where to go from there.

Any help is appreciated!
Thanks.
1. to use the double angle formulae, you need the value of $\cos{x}$ and the quadrant that x resides (III or IV, since $\sin{x} < 0$). use the Pythagorean identity or a reference triangle to find the value of $\cos{x}$

2. "Find the exact value of the trig function ... "

what trig function? Is there more information to this question?

3. $\cos{x}(1 + 2\sin{x}) = 0$

set each factor equal to zero ...

$\cos{x} = 0$ , $1 + 2\sin{x} = 0$

solutions for x will be angles from the unit circle ...

for the first factor, $\cos{x} = 0$ at $x = \frac{\pi}{2}$ and $\frac{3\pi}{2}$

you solve for the second factor.