Question

What is cos θ when sin θ = 2/5? Rationalize the denominator if necessary.

Answer 1

`cos(\theta)=(√(21))/(5)`

Explanation:

we have that

The angle
`\theta` belong the the First Quadrant (see the figure)

so

`cos(\theta)\ and\ sin(\theta)` are positive values

we know that

`sin^2(\theta)+cos^2(\theta)=1` ----> trigonometric identity

we have

`sin(\theta)=(2)/(5)`

substitute in the identity

`((2)/(5))^2+cos^2(\theta)=1`

`cos^2(\theta)=1-(4)/(25)`

`cos^2(\theta)=(21)/(25)`

square root both sides

`cos(\theta)=(√(21))/(5)`