alleryStart learning →sin(2θ) equals:
- 2 sin θ cos θ
- sin²θ - cos²θ
- sin θ + cos θ
- 2 sin θ
Show answer and solution
Correct answer: A. 2 sin θ cos θ
**Double-angle formula:** sin(2θ) = 2 sinθ cosθ.
(Derived from sin(θ + θ).)
Indian Navy Pilot Vectors & 3D Geometry — practice questions
Explore 74 free Vectors & 3D Geometry questions in Indian Navy Pilot Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Vectors & 3D Geometry with Quill →Vectors & 3D Geometry questions and exercises with answers
Showing questions 1–30 of 74.
sin(2θ) equals:Read the answer and worked solution →In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:Read the answer and worked solution →The distance between the points $(1,2)$ and $(1,5)$ is:Read the answer and worked solution →Find the midpoint of A(2, −3) and B(8, 5).Read the answer and worked solution →The angle θ between two PLANES with normals n1 and n2 satisfies: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 →
Worked practice questions
In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:
- a/sinA = b/sinB = c/sinC
- a + b + c = 0
- sinA = sinB
- a²+b² = c²
Show answer and solution
Correct answer: A. a/sinA = b/sinB = c/sinC
**Sine rule:** a/sinA = b/sinB = c/sinC = 2R (where R is circumradius).
Useful for solving triangles when you know any side + opposite angle + one more piece.
The distance between the points $(1,2)$ and $(1,5)$ is:
- 6
- 3
- 5
- 4
Show answer and solution
Correct answer: B. 3
Same x, so distance = |5−2| = 3.
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