Question

part b: calculations - round all answers to 1 decimal place

1. if tan b = \frac{11}{15}, find the measure of b. 1 mark
2. if cos a = - 0.56, find the measure of a. 1 mark

Explanation:

Question 6

Step1: Use inverse tangent function

We know that if \(\tan B=\frac{11}{15}\), then \(B = \tan^{- 1}(\frac{11}{15})\)

Step2: Calculate using calculator

Using a calculator, \(\tan^{-1}(\frac{11}{15})\approx36.0^{\circ}\)

Step1: Use inverse cosine function

Since \(\cos A=- 0.56\), then \(A=\cos^{-1}(-0.56)\)

Step2: Calculate using calculator

Using a calculator, \(\cos^{-1}(-0.56)\approx124.1^{\circ}\) (because \(\cos\theta=\cos(360 - \theta)\), but in the range of \(0^{\circ}\leq\theta\leq180^{\circ}\) for the principal value of inverse cosine when the cosine value is negative)

Answer:

\(36.0^{\circ}\)

Question 7