Recover an acute angle
Use the inverse key matching the given ratio and set degree mode. The inverse notation does not mean taking a reciprocal
- Choose the matching inverse The stated ratio names the key. Inverse sine, inverse cosine and inverse tangent each recover an angle from their own ratio \(\displaystyle \begin{aligned}\sin\theta=v&\;\Longrightarrow\;\theta=\sin^{-1}(v)\\\cos\theta=v&\;\Longrightarrow\;\theta=\cos^{-1}(v)\\\tan\theta=v&\;\Longrightarrow\;\theta=\tan^{-1}(v)\end{aligned}\)
- Use degree mode The inverse key returns an angle. Degree mode gives the requested angle unit
- Round the final angle Enter the complete supplied ratio. Keep the calculator output until you round the answer to the requested precision
Worked example
Find the acute angle to one decimal place in degree mode
- \(\displaystyle \theta=\sin^{-1}(0.718)\)The given ratio is sine, so choose inverse sine
- \(\displaystyle \theta=45.889602\ldots^{\circ}\)Use the complete stated value and keep the calculator output
- \(\displaystyle \theta\approx45.9^{\circ}\)Round once to one decimal place
Common mistakes
Difficulty levels
Questions about this topic
What does the inverse key return?+
It returns the angle with the given trigonometric value. In degree mode the output is measured in degrees
Can I enter a tangent value greater than one?+
Yes. Acute tangent values can exceed one. Acute sine and cosine values lie strictly between zero and one
Should I change a supplied rounded ratio?+
No. Use the complete value printed in the question. That is the input from which the answer is calculated
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 9 Mathematics, chapter 3: Pythagoras and trigonometry