Question

calculator practice using sine, cosine, and tangent (round to the nearest hundredth)

sin(30°) = ________
cos(45°) = ________
tan(50°) = ________
sin(90°) = ________
cos(0°) = ________
tan(25°)=________

trigonometric ratios
sinθ = \frac{opposite}{hypotenuse}
cosθ = \frac{adjacent}{hypotenuse}
tanθ = \frac{opposite}{adjacent}

ex 1: given the right triangle below, set up a trigonometric ratio to find the missing side x.

3
38.7°
x

Explanation:

Step1: Identify the trigonometric ratio

We know the side opposite the angle ($3$) and we want to find the hypotenuse ($x$). Using the sine ratio ($\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$). Here $\theta = 38.7^{\circ}$, opposite $=3$, hypotenuse $=x$.
So, $\sin(38.7^{\circ})=\frac{3}{x}$.

Step2: Solve for $x$

Cross - multiply to get $x\times\sin(38.7^{\circ})=3$. Then $x=\frac{3}{\sin(38.7^{\circ})}$.
Using a calculator, $\sin(38.7^{\circ})\approx0.625$.
So, $x=\frac{3}{0.625}=4.8$.

Answer:

$x = 4.8$