alleryStart learning →Value of arccos(-1):
- -π
- π/2
- 0
- π
Show answer and solution
Correct answer: D. π
cos(π) = -1, so arccos(-1) = π.
(Principal range [0, π].)
Indian Navy INET Inverse Trigonometric Functions — practice questions
Explore 28 free Inverse Trigonometric Functions questions in Indian Navy INET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Inverse Trigonometric Functions with Quill →Inverse Trigonometric Functions questions and exercises with answers
Showing questions 1–28 of 28.
Value of arccos(-1):Read the answer and worked solution →$\tan^{-1}\left(\tfrac{1}{2}\right) + \tan^{-1}\left(\tfrac{1}{3}\right)$ equalsRead the answer and worked solution →Sort each inverse function into its domainRead the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Put the reasoning in order: why an inverse needs a restricted domainRead the answer and worked solution →True or false: existence of inversesRead the answer and worked solution →True or false: reading the tableRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Complete the summary tableRead the answer and worked solution →Complete the rule about restricting a domainRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Principal values worked in the chapterRead the answer and worked solution →Order the steps for finding a principal valueRead the answer and worked solution →True or false: principal valuesRead the answer and worked solution →Match each identity to the condition it needsRead the answer and worked solution →Assertion and reason: identitiesRead the answer and worked solution →Match each mathematician to the year your syllabus givesRead the answer and worked solution →Trace how trigonometry travelledRead the answer and worked solution →True or false: the historical noteRead the answer and worked solution →
Worked practice questions
$\tan^{-1}\left(\tfrac{1}{2}\right) + \tan^{-1}\left(\tfrac{1}{3}\right)$ equals
- $\tfrac{\pi}{2}$
- $\tfrac{\pi}{3}$
- $\tfrac{\pi}{4}$
- $\pi$
Show answer and solution
Correct answer: C. $\tfrac{\pi}{4}$
Since $\tfrac{1}{2}\cdot\tfrac{1}{3} = \tfrac{1}{6} < 1$, apply $\tan^{-1}x + \tan^{-1}y = \tan^{-1}\tfrac{x+y}{1-xy}$.
Here $\tfrac{x+y}{1-xy} = \tfrac{\tfrac{1}{2}+\tfrac{1}{3}}{1 - \tfrac{1}{6}} = \tfrac{5/6}{5/6} = 1$
so the sum is $\tan^{-1}(1) = \tfrac{\pi}{4}$.
Sort each inverse function into its domain
Read exercise and reference answers
- Items
- Item
- sin⁻¹ x
- Category
- [−1, 1]
- Item
- cos⁻¹ x
- Category
- [−1, 1]
- Item
- cosec⁻¹ x
- Category
- R − (−1, 1)
- Item
- sec⁻¹ x
- Category
- R − (−1, 1)
- Item
- tan⁻¹ x
- Category
- R
- Item
- cot⁻¹ x
- Category
- R
- Categories
- Item
- [−1, 1]
- Item
- R − (−1, 1)
- Item
- R
Only sin⁻¹ and cos⁻¹ accept every value from −1 to 1. cosec⁻¹ and sec⁻¹ need |x| ≥ 1, so the open middle is cut out.
tan⁻¹ and cot⁻¹ accept any real number.
Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.
How to practise
- Choose a Inverse Trigonometric Functions question and try to work out your answer.
- Open the question to check the correct answer and read its worked solution.
- Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.