Answers: Trigonometry (radians)

Summary

Answers to the questions on trigonometry, using radians to measure angles.

These are the answers to Questions: Trigonometry (radians).

Please attempt the questions before reading these answers!

Q1

You are given the triangle below.

Q1. Triangle

Here,

• $\cos (a)={\displaystyle \frac{4}{5}}$

• $\sin (a)={\displaystyle \frac{3}{5}}$

• $\tan (a)={\displaystyle \frac{3}{4}}$

• $\cos (b)={\displaystyle \frac{3}{5}}$

• $\sin (b)={\displaystyle \frac{4}{5}}$

• $\tan (b)={\displaystyle \frac{4}{3}}$

Q2

Using the triangle below, solve the following equations.

Q2. Triangle

2.1. $C=12$

2.2. $A=2$

2.3. $A=1.812$ (to three decimal places)

2.4. $A=\sqrt{6}$

2.5. $A=8$

2.6. $B=\frac{8}{\sqrt{3}}$.

Q3

3.1. $\cos (\pi /6)={\displaystyle \frac{\sqrt{3}}{2}}$

3.2. $\tan (\pi /6)={\displaystyle \frac{1}{\sqrt{3}}}={\displaystyle \frac{\sqrt{3}}{3}}$

3.3. $\csc (\pi /4)=1$

3.4. $\cot (\pi /6)-\sin (\pi /3)=\sqrt{3}-{\displaystyle \frac{\sqrt{3}}{2}}={\displaystyle \frac{\sqrt{3}}{2}}$

3.5. $\sin (\pi /2)+\cos (\pi )=1+(-1)=0$

3.6. $\tan (\pi /6)-\cot (\pi /6)=\frac{1}{\sqrt{3}}-\sqrt{3}$

3.7. $\cos (0)\sin (\pi /2)=1\cdot 1=1$

3.8. $\cos (\pi /6)\sec (\pi /6)-\sin (\pi /4)\csc (\pi /4)=1-1=0$

3.9. $\cot (\pi /2)=0$

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Version history and licensing

v1.0: initial version created 08/23 by Dzhemma Ruseva, Ellie Gurini, Ciara Cormican as part of a University of St Andrews STEP project.

• v1.1: edited 05/24 by tdhc, and split into versions for both degrees and radians.

This work is licensed under CC BY-NC-SA 4.0.