Question

If the sinø=7/12, what is cosø?

Answer 1

Answer:

If the sinø=7/12, cosø is $\frac{\sqrt{95} }{12}$

Step-by-step explanation:

We are given sinФ = 7/12

We need to find cosФ

The basic trigonometric functions of right triangle are:

$sin\theta=\frac{opposite}{hypotenuse}$

$cos\theta=\frac{adjacent}{hypotenuse}$

We need values of adjacent and hypotenuse to find cosФ

Using Pythagoras theorem we can find the value of adjacent

$(Hypotenuse)^2= (Opposite)^2+(Adjacent)^2$

We have Hypotenuse= 12 and Opposite = 7 (because $sin\theta=\frac{opposite}{hypotenuse}$ and we are given $sin\theta=\frac{7}{12}$

Inserting values and finding adjacent:

$(Hypotenuse)^2= (Opposite)^2+(Adjacent)^2\\(12)^2=(7)^2+(Adjacent)^2\\144=49+(Adjacent)^2\\144-49=(Adjacent)^2\\95=(Adjacent)^2\\\sqrt{(Adjacent)^2} =\sqrt{95}\\Adjacent=\sqrt{95}$

So, value of Adjacent is $\sqrt{95}$

Now finding cosФ

$cos\theta=\frac{adjacent}{hypotenuse}$

Adjacent = $\sqrt{95}$, hypotenuse = 12

$cos\theta=\frac{\sqrt{95} }{12}$

So, If the sinø=7/12, cosø is $\frac{\sqrt{95} }{12}$