Answer:
If the sinø=7/12, cosø is [tex]\frac{\sqrt{95} }{12}[/tex]
Step-by-step explanation:
We are given sinФ = 7/12
We need to find cosФ
The basic trigonometric functions of right triangle are:
[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]
[tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex]
We need values of adjacent and hypotenuse to find cosФ
Using Pythagoras theorem we can find the value of adjacent
[tex](Hypotenuse)^2= (Opposite)^2+(Adjacent)^2[/tex]
We have Hypotenuse= 12 and Opposite = 7 (because [tex]sin\theta=\frac{opposite}{hypotenuse}[/tex] and we are given [tex]sin\theta=\frac{7}{12}[/tex]
Inserting values and finding adjacent:
[tex](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}[/tex]
So, value of Adjacent is [tex]\sqrt{95}[/tex]
Now finding cosФ
[tex]cos\theta=\frac{adjacent}{hypotenuse}[/tex]
Adjacent = [tex]\sqrt{95}[/tex], hypotenuse = 12
[tex]cos\theta=\frac{\sqrt{95} }{12}[/tex]
So, If the sinø=7/12, cosø is [tex]\frac{\sqrt{95} }{12}[/tex]
