Question

1. solve for each of the following using the informsin: $\frac{4.0}{4.0} rightarrow \frac{2.8}{4.0}$cosine: $\frac{4.9}{4.9} rightarrow \frac{4.0}{4.9}$tan: $\frac{2.8}{4.0}$

Explanation:

Step1: Define sine of 35°

For the 35° angle, $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin(35^\circ)=\frac{2.8}{4.9}$

Step2: Simplify sine fraction

Divide numerator and denominator by 0.7.
$\sin(35^\circ)=\frac{4}{7}\approx0.571$

Step3: Define cosine of 35°

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos(35^\circ)=\frac{4.0}{4.9}$

Step4: Simplify cosine fraction

Divide numerator and denominator by 0.1.
$\cos(35^\circ)=\frac{40}{49}\approx0.816$

Step5: Define tangent of 35°

$\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan(35^\circ)=\frac{2.8}{4.0}$

Step6: Simplify tangent fraction

Divide numerator and denominator by 0.4.
$\tan(35^\circ)=\frac{7}{10}=0.7$

Answer:

$\sin(35^\circ)=\frac{2.8}{4.9}\approx0.571$, $\cos(35^\circ)=\frac{4.0}{4.9}\approx0.816$, $\tan(35^\circ)=\frac{2.8}{4.0}=0.7$