Question

question 4
calculate the following:
a) $\sin(167.9^{\circ}) = 0.2096$
b) $\cos(35.3^{\circ}) = 0.8161$
c) $\tan(205.5^{\circ}) = $
enter an integer or decimal number more..
d) $\sin^{-1}(0.5256) = $
e) $\cos^{-1}(0.1557) = $
f) $\tan^{-1}(0.2444) = $
round all ratios to 4 decimal places and angles to 1 decimal place.

Explanation:

Step1: Calculate \(\tan(205.5^{\circ})\)

Use the identity \(\tan(\theta)=\tan(\theta - 180^{\circ})\) when \(\theta> 180^{\circ}\). So \(\tan(205.5^{\circ})=\tan(205.5^{\circ}-180^{\circ})=\tan(25.5^{\circ})\). Using a calculator, \(\tan(25.5^{\circ})\approx0.4767\)

Step2: Calculate \(\sin^{-1}(0.5256)\)

Using a calculator, \(\sin^{-1}(0.5256)\approx31.7^{\circ}\)

Step3: Calculate \(\cos^{-1}(0.1557)\)

Using a calculator, \(\cos^{-1}(0.1557)\approx81.0^{\circ}\)

Step4: Calculate \(\tan^{-1}(0.2444)\)

Using a calculator, \(\tan^{-1}(0.2444)\approx13.7^{\circ}\)

Answer:

c) \(0.4767\)
d) \(31.7^{\circ}\)
e) \(81.0^{\circ}\)
f) \(13.7^{\circ}\)