Find the possible values of $\sin\theta$ and $\tan\theta$, given that $\cos\theta = 3/5$ and $0 \leq \theta \leq \pi/2$.
Here is my working out:
Using a right hand triangle:
$$\cos\theta =a/c$$
$$\cos\theta =3/5$$
$$a^2 = b^2 + c^2$$
$$5^2= 3^2+ b^2$$
Therefore $b=+ 4$ or $- 4$.
Compute the values of $b$ and $c$ to find $\sin\theta$
$$\sin\theta = b/ c = 4/5$$
$$\tan\theta = \sin/\cos = (3/5) / (4/5)$$
$$\tan\theta = 4/5.$$
Is this right?
Or is it better to do this is in a graph?
Best Answer
That's right. I think you should specify what's wrong with $b=-4$ though. The question says that $\theta$ has to be between 0 and $\pi/2$. That's the problem. Also just to clarify, it should be sin $\theta$ and tan $\theta$, not just sin and tan. The way I see it is that it's like writing the square root sign without anything underneath. Actually yes, tan$\theta$ should be 4/3.