Class 12 Inverse Trigonometric Functions · Long Answer3 Marksprincipal_values
Class 12 Maths · Inverse Trigonometric Functions · Long Answer #97
Evaluate \(\cos^{-1}[\cos(680^\circ)]\), giving radians.
✅ Step-by-Step Solution
Final Answer: 2π/9
- Reduce 680° modulo 360° to 320°.
- By cosine symmetry, cos320°=cos(360°−40°)=cos40°.
- The angle 40° lies in the principal arccosine interval [0°,180°], so the inverse returns 40°.
- Therefore the value is 40°=2π/9 radians.
📋 CBSE Stepwise Marking Scheme
- [0.5 marks] Reduce 680° modulo 360° to 320°.
- [1 mark] By cosine symmetry, cos320°=cos(360°−40°)=cos40°.
- [1 mark] The angle 40° lies in the principal arccosine interval [0°,180°], so the inverse returns 40°.
- [0.5 marks] Therefore the value is 40°=2π/9 radians.
Master Chapter 2: Inverse Trigonometric Functions
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Inverse Trigonometric Functions.
← Previous Question
For x>0, solve \(\tan[\sec^{-1}(1/x)]=\sin(\tan^{-1}2)\).
Next Question →Prove \(\sec^2(\tan^{-1}2)+\operatorname{cosec}^2(\cot^{-1}5)=31\).
More Practice Questions in Inverse Trigonometric Functions
Related Questions in Inverse Trigonometric Functions
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
Evaluate \(\sin^{-1}(\cos(13\pi/5))\).
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
Find the full real solution set of \(\sin^{-1}x>\cos^{-1}x\).
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
Evaluate \(\sin[\pi/2-\sin^{-1}(-1/2)]\).
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
For \(x\in[-1,1]\setminus\{0\}\), simplify \(\cot(\sin^{-1}x)\).
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
Evaluate \(\sin^{-1}(\cos(\pi/9))\).
Class 12 Inverse Trigonometric Functions · Mcq Single Correct
Evaluate \(\theta=\sin^{-1}(\sin(-600^\circ))\), giving the answer in radians.