I have a question where I have to solve for the cos, tan, csc, sec, and cot when given a value of sin(theta). One of them is like this:
sin(theta) = 1/3 0 < theta < pi/2
Not a clue where to go with this.
Any help would be appreciated.
I have a question where I have to solve for the cos, tan, csc, sec, and cot when given a value of sin(theta). One of them is like this:
sin(theta) = 1/3 0 < theta < pi/2
Not a clue where to go with this.
Any help would be appreciated.
$\displaystyle \sin \theta = \frac{1}{3} \ \ \ \ 0 < \theta < \frac{\pi}{2}$
You are looking for ratios in the 1st quadrant.
$\displaystyle \sin \theta=\frac{y}{r} \ \ \ \ \csc\theta=\frac{r}{y}$
$\displaystyle \cos \theta=\frac{x}{r} \ \ \ \ \sec\theta=\frac{r}{x}$
$\displaystyle \tan\theta=\frac{y}{x} \ \ \ \ \cot\theta=\frac{x}{y}$
You already know r and y. Use $\displaystyle r^2=x^2+y^2$ to find x.
Then, you can find all the other ratios.