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Published on: 26/08/2019
Trigonometric Functions
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Questions + Answers key
Take MCQ Mathematics Test
1.
Find the general solutions of\(\sqrt{3}\) sin x-cos x =2 ______.
X = n\(\pi +{\pi\over 6}+(-1)^n{\pi\over2}\)
X = n\(\pi -{\pi\over 6}+(-1)^n{\pi\over2}\)
X = n\(\pi +{\pi\over 6}+(-1)^{n+1}{\pi\over2}\)
None
2.
The solution of the equation cos2 \(\theta\) -+sin\(\theta\)+ 1=0lies in the interval ______.
\(({\pi\over 4},{3\pi\over4})\)
\((-{\pi\over 4},{3\pi\over4})\)
\(({3\pi\over 4},{5\pi\over4})\)
\(({5\pi\over 4},{7\pi\over4})\)
3.
If 4 sin2\(\theta=1\) then the values of \(\theta\) are ______.
\(2n\pi\pm{\pi\over3},n\in Z\)
\(n\pi\pm{\pi\over3},n\in Z\)
\(n\pi\pm{\pi\over6},n\in Z\)
\(2n\pi\pm{\pi\over6},n\in Z\)
4.
If A, B, C are in A.P. then \({sinA-sinC\over cosC-cosA}\) is equal to ______.
sin B
cot B
sin 2B
cot 2B
5.
If sin \(\theta\) + sin \(\phi\)= \(\alpha\) and cos\(\theta\) - cos\(\phi\)= b then tan\({\theta -\phi\over 2}\) is equal to ______.
\(\sqrt{a^2+b^2}\)
\(-{a\over b}\)
\(-{b\over a}\)
\(1\over \sqrt{a^2-b^2}\)
6.
In a\(\triangle\) ABC, if tan A +tanB+ tan C = o then cot A cot B cot C is equal to______.
6
3
\(1\over6\)
\(1\over3\)
7.
If tan \(\theta={\alpha\over \alpha+1}\) and tan \(\phi ={1\over 2\alpha+1}\) , then (A+ B) is equal to ______.
0
\(\pi\over4\)
\(\pi\over6\)
\(\pi\over2\)
8.
If tan \(\theta\) + sec \(\theta\) = ex then cos\(\theta\) is equal to ______.
\({e^x+e^{-x}\over 2}\)
\({e^x-e^{-x}\over 2}\)
\({e^x-e^{-x}\over e^x+e^x}\)
\({2\over e^x+e^{-x}}\)
9.
If tan\(\theta\) + cot \(\theta\) = 5 then tan3 \(\theta\) + cot3 \(\theta\) is equal to ______.
135
140
110
90
10.
sin6\(\theta\) + cos6\(\theta\) + 3 sin2\(\theta\) cos2\(\theta\) is equal to ______.
0
1
4
2
11.
If x = r sin\(\alpha\) cos \(\beta\), y = r sin\(\alpha\) sin \(\beta\)and z = r cos\(\alpha\), then X2 + y2 + Z2 is independent of ______.
\(\alpha , \beta\)
\(\gamma , \alpha\)
\(\gamma , \beta\)
none of these
12.
In a ΔABC, if the sides are 7cm, 4\(\sqrt { 3 } \) cm and .\(\sqrt { 13 } \) cm, then the smallest angle is ______.
45o
60o
30o
90o
13.
In a ΔABC if a = 5, b = 6 and c = 5, then ∠B is ______.
cos-1 \(\left( \frac { 7 }{ 24 } \right) \)
cos-1\(\left( \frac { 7 }{ 25 } \right) \)
cos-1 \(\left( \frac { 7 }{30 } \right) \)
None
14.
In a ∆ABC, if ∠A = 45o, ∠B = 60o and ∠C = 75o, then the ratio of sides is ______.
2 : \(\sqrt { 6 } :(\sqrt { 3 } +1)\)
\(\sqrt { 2 } :6:(\sqrt { 3 } +1)\)
\(2:\sqrt { 6 } :(\sqrt { 3 } -1)\)
None
1.
(a)
X = n\(\pi +{\pi\over 6}+(-1)^n{\pi\over2}\)
2.
(d)
\(({5\pi\over 4},{7\pi\over4})\)
3.
(c)
\(n\pi\pm{\pi\over6},n\in Z\)
4.
(b)
cot B
5.
(c)
\(-{b\over a}\)
6.
(c)
\(1\over6\)
7.
(b)
\(\pi\over4\)
8.
(d)
\({2\over e^x+e^{-x}}\)
9.
(c)
110
10.
(b)
1
11.
(a)
\(\alpha , \beta\)
12.
(c)
30o
13.
(b)
cos-1\(\left( \frac { 7 }{ 25 } \right) \)
14.
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