Question

The terminal side of an angle θ in standard position is in quadrant 1. If sinθ=0.8, find cosθ.

Answer 1

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

Explanation:

Since
`sin\theta=0.8` is the same as
`sin\theta=(4)/(5)` and
`sin\theta=(opposite)/(hypotenuse)`, then we know that the side opposite to the angle
`\theta` is 4 units and the hypotenuse is 5 units.

Because
`cos\theta=(adjacent)/(hypotenuse)`, then we have to find the adjacent side to the angle
`\theta` using the Pythagorean Theorem:

`a^2+b^2=c^2\\\\(adjacent)^2+(opposite)^2=(hypotenuse)^2\\\\(adjacent)^2+4^2=5^2\\\\(adjacent)^2+16=25\\\\(adjacent)^2=9\\\\adjacent=3`

Therefore, since the adjacent side is 3 units, then
`cos\theta=(3)/(5)`