alleryStart learning →sec θ is defined as:
- 1/sin θ
- sin θ/cos θ
- 1/tan θ
- 1/cos θ
Show answer and solution
Correct answer: D. 1/cos θ
sec θ = 1/cos θ (cosecant: csc θ = 1/sin θ; cotangent: cot θ = 1/tan θ).
Indian Navy 10+2 B.Tech Cadet Trigonometry — practice questions
Explore 28 free Trigonometry questions in Indian Navy 10+2 B.Tech Cadet Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Trigonometry with Quill →Trigonometry questions and exercises with answers
Showing questions 1–28 of 28.
sec θ is defined as:Read the answer and worked solution →General solution of cos θ = 0:Read 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
General solution of cos θ = 0:
- θ = π/2 + nπ
- θ = nπ
- θ = π/4 + nπ
- θ = 0 + 2nπ
Show answer and solution
Correct answer: A. θ = π/2 + nπ
cos θ = 0 at θ = π/2 and 3π/2 (i.e., 90° and 270°).
**General:** θ = π/2 + nπ where n ∈ ℤ. (Every π apart.)
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.
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