Sail E0 Webinar

Quantitative Aptitude

TRIGONOMETRY MCQs

Total Questions : 420 | Page 6 of 42 pages
Question 51. If $${\text{2cos}}\theta - \sin \theta = \frac{1}{{\sqrt 2 }},$$    $$\left( {{0^ \circ } < \theta < {{90}^ \circ }} \right)$$   the value of $$2\sin \theta $$  + $$\cos \theta $$   is?
  1.    $$\frac{1}{{\sqrt 2 }}$$
  2.    $$\sqrt 2 $$
  3.    $$\frac{3}{{\sqrt 2 }}$$
  4.    $$\frac{1}{{\sqrt 3 }}$$
 Discuss Question
Answer: Option C. -> $$\frac{3}{{\sqrt 2 }}$$
Question 52. If sec2θ + tan2θ = 7, then the value of θ when 0° ≤ θ ≤ 90° is?
  1.    60°
  2.    30°
  3.    0°
  4.    90°
 Discuss Question
Answer: Option A. -> 60°
Question 53. The simplified value of (sec x sec y + tan x tan y)2 - (sec x tan y + tan x sec y)2
  1.    -1
  2.    0
  3.    sec2 x
  4.    1
 Discuss Question
Answer: Option D. -> 1
Question 54. If A = sin2θ + cos4θ for any value of θ, then the value of A is?
  1.    $${\text{1}} \leqslant {\text{A}} \leqslant {\text{1}}$$
  2.    $$\frac{3}{4} \leqslant {\text{A}} \leqslant {\text{1}}$$
  3.    $$\frac{{13}}{{16}} \leqslant {\text{A}} \leqslant {\text{1}}$$
  4.    $$\frac{3}{4} \leqslant {\text{A}} \leqslant \frac{{13}}{{16}}$$
 Discuss Question
Answer: Option B. -> $$\frac{3}{4} \leqslant {\text{A}} \leqslant {\text{1}}$$
Question 55. In circular measure, the value of the angle 11° 15' is?
  1.    $$\frac{{{\pi ^c}}}{{16}}$$
  2.    $$\frac{{{\pi ^c}}}{8}$$
  3.    $$\frac{{{\pi ^c}}}{4}$$
  4.    $$\frac{{{\pi ^c}}}{{12}}$$
 Discuss Question
Answer: Option A. -> $$\frac{{{\pi ^c}}}{{16}}$$
Question 56. In a triangle ABC, ∠ABC = 75° and ∠ACB = $$\frac{{{\pi ^c}}}{4},$$  the circular measure of ∠BAC is?
  1.    $$\frac{{5\pi }}{{12}}$$ radian
  2.    $$\frac{\pi }{3}$$ radian
  3.    $$\frac{\pi }{6}$$ radian
  4.    $$\frac{\pi }{2}$$ radian
 Discuss Question
Answer: Option B. -> $$\frac{\pi }{3}$$ radian
Question 57. If a right-angled triangle XYZ right-angled at Y. If XY = $${\text{2}}\sqrt 6 $$  and XZ - YZ = 2, then secX + tanX is?
  1.    $$\frac{1}{{\sqrt 6 }}$$
  2.    $$\sqrt 6 $$
  3.    $$2\sqrt 6 $$
  4.    $$\frac{{\sqrt 6 }}{2}$$
 Discuss Question
Answer: Option B. -> $$\sqrt 6 $$
Question 58. If $$\theta $$ be acute angle and $$\cos \theta = \frac{{15}}{{17}}{\text{,}}$$   then the value of $${\text{cot}}\left( {{{90}^ \circ } - \theta } \right)$$   is?
  1.    $$\frac{{2\sqrt 8 }}{{15}}$$
  2.    $$\frac{8}{{15}}$$
  3.    $$\frac{{\sqrt 2 }}{{17}}$$
  4.    $$\frac{{8\sqrt 2 }}{{17}}$$
 Discuss Question
Answer: Option B. -> $$\frac{8}{{15}}$$
Question 59. In ΔABC, ∠B = 90° and AB : BC = 2 : 1, then value of (sinA + cotC) = ?
  1.    $$3 + \sqrt 5 $$
  2.    $$\frac{{2 + \sqrt 5 }}{{2\sqrt 5 }}$$
  3.    $$2 + \sqrt 5 $$
  4.    $$3\sqrt 5 $$
 Discuss Question
Answer: Option B. -> $$\frac{{2 + \sqrt 5 }}{{2\sqrt 5 }}$$
Question 60. If sin21° = $$\frac{x}{y}{\text{,}}$$  then sec21° - sin69° is equal to?
  1.    $$\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }}$$
  2.    $$\frac{{{y^2}}}{{x\sqrt {{y^2} - {x^2}} }}$$
  3.    $$\frac{{{x^2}}}{{y\sqrt {{x^2} - {y^2}} }}$$
  4.    $$\frac{{{y^2}}}{{x\sqrt {{x^2} - {y^2}} }}$$
 Discuss Question
Answer: Option A. -> $$\frac{{{x^2}}}{{y\sqrt {{y^2} - {x^2}} }}$$

Latest Videos

Latest Test Papers