Question

the point (3,4) is on the the terminal side of angle Theta, in standard position. What are the values of sine, cosine and tangent of theta?

Answer 1

Since the angle is in standard position we can, we draw a right triangle for this point.

See diagram.

Using Pythagoras Theorem, we find the hypotenuse


`h^(2) =3^(2) +4^(2)`


`\Rightarrow h^(2) =9 +16`


`\Rightarrow h^(2) =25`


`\Rightarrow h=√(25)`


`\Rightarrow h= 5 \ units`

Now recall the mnemonics SOH CAH TOA


`\sin(\theta)=(opposite)/(hypotenuse)`


`\Rightarrow \sin(\theta)=(4)/(5)`


`\cos(\theta)=(adjacent)/(hypotenuse)`


`\Rightarrow \cos(\theta)=(3)/(5)`

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