Question

Suppose that cos(θ)=20/29 and 0≤θ≤π/2.Sketch a right triangle with an interior angle measure of θ radians. Since cos(θ)=20/29, you can write down the lengths of two sides of the right triangle.Using your diagram from part (a), determine the exact value of sin(θ). Enter your answer as a fraction.sin(θ)= Using your diagram from part (a), determine the exact value of tan(θ). Enter your answer as a fraction.tan(θ)=

Answer 1

ANSWERS

a.

b. sin(θ) = 21/29

c. tan(θ) = 21/20

Step-by-step explanation

For any right triangle the trigonometric ratios are:

`\cos \theta=\frac{\text{adjacent}}{\text{ hypotenuse}}`
`\sin \theta=\frac{\text{opposite}}{\text{ hypotenuse}}`
`\tan \theta=(\sin \theta)/(\cos \theta)=\frac{\text{ opposite}}{\text{ adjacent}}`

We know the hypotenuse and the adjacent, we want to know the opposite. We can find it using the Pythagorean theorem:

`\begin{gathered} h^2=(\text{adjacent)}^2+(\text{opposite)}^2 \\ 29^2=20^2+(\text{opposite)}^2 \\ \text{opposite}=\sqrt[]{29^2-20^2} \\ \text{opposite}=\sqrt[]{441} \\ \text{opposite}=21 \end{gathered}`

The sine of the angle is:

`\sin \theta=(21)/(29)`

The tangent is:

`\tan \theta=(21)/(20)`