# If cos(θ)=3/5, what is the value of sin(θ)?

## Just a math question I don't get. Also, it is one of those questions where its "click all that apply" so there might be more then one answer I guess. Please and Thanks :) Mar 1, 2018

$\pm \frac{4}{5}$

#### Explanation:

We have: $\cos \theta = \frac{3}{5}$

Using the Pythagorean identity,

${\cos}^{2} \theta + {\sin}^{2} \theta = 1$

So.

$\frac{9}{25} + {\sin}^{2} \theta = 1$

${\sin}^{2} \theta = 1 - \frac{9}{25}$

$= \frac{16}{25}$

$\therefore \sin \theta = \sqrt{\frac{16}{25}}$

$= \pm \frac{4}{5}$

Mar 1, 2018

The value is $\frac{4}{5}$

#### Explanation:

We know from the given that cos(θ)= 3/5 So then to simplify further, we will divide:
cos(θ)= 3/5 rarr cos(θ) = 0.6
Since we want to find the value of θ, we have to use the inverse operation on the calculator. We want to figure out which angle (that has the value of θ in this example) resulted in a cosine of 0.6.
cos(θ) = 0.6 (hit $2 n d$ button then hit $\cos$ button)
θ ~~ 53.13

Now that we know that value of θ, we are able to plug that in to the other equation.
sin(θ) = x rarr sin(53.13) = x
Now use the normal $\sin$ button on your calculator to find the value of $x$
$\sin \left(53.13\right) \approx 0.8$ or $\frac{4}{5}$