Question

for help with question 2, refer to example 2. 2. evaluate. round your answers to four decimal places. a) sin 30° b) cos 45° d) tan 60°

Explanation:

Part (a): Evaluate $\sin 30^\circ$

Step1: Recall the value of $\sin 30^\circ$

We know from trigonometric ratios that $\sin 30^\circ=\frac{1}{2}$.

Step2: Convert to decimal and round

$\frac{1}{2} = 0.5$. Rounding to four decimal places, we get $0.5000$.

Step1: Recall the value of $\cos 45^\circ$

We know that $\cos 45^\circ=\frac{\sqrt{2}}{2}$.

Step2: Calculate the decimal value

$\frac{\sqrt{2}}{2}\approx\frac{1.41421356}{2}= 0.70710678$.

Step3: Round to four decimal places

Rounding $0.70710678$ to four decimal places, we look at the fifth decimal place which is $0$. Since $0\lt5$, we keep the fourth decimal place as it is. So we get $0.7071$.

Step1: Recall the value of $\tan 60^\circ$

We know that $\tan 60^\circ = \sqrt{3}$.

Step2: Calculate the decimal value

$\sqrt{3}\approx1.73205081$.

Step3: Round to four decimal places

Rounding $1.73205081$ to four decimal places, we look at the fifth decimal place which is $5$. Since $5\geq5$, we round up the fourth decimal place. So $1.7320 + 0.0001=1.7321$.

Answer:

$0.5000$

Part (b): Evaluate $\cos 45^\circ$