Having trouble getting a start on this problem, any help would be appreciated!
Given point $P = (-3,5)$ is on the terminal arm of angle $\theta$ in standard position. Calculate the exact value of $\sin\theta, \cos\theta$, and $\tan\theta$.
[Math] Calculate Exact Value of $\sin\theta, \cos\theta$ and $\tan\theta$
trigonometry
Best Answer
Hints:
What quadrant is the point $\;P = ({\bf x, y}) = (-3, 5)$ located?
Draw the right triangle that point $P$ makes with the $x$ axis - the length of the hypotenuse of the right triangle will equal $\;{\bf h} = \sqrt{(-3)^2 + 5^2} = \sqrt{34}$
Use SOH CAH TOA to unpack the definitions of $\tan \theta, \;\sin\theta,\;\cos\theta$:
$$\tan\theta = \frac{\text{opposite}}{\text{adjacent}} = \frac yx = \quad?\;$$ $$\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac yh = \quad?\;$$ $$\cos \theta= \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{x}{h} = \quad?$$