Trigonometry Questions and answers

  1. Elementary Mathematics
    1. Quadratic Equations
    2. Simplification
    3. Area and perimeter
    4. Volume and surface area
    5. Geometry
    6. Trigonometry
    7. Polynomials
    8. Height and Distance
    9. Simple and Decimal fraction
    10. Indices and Surd
    11. Logarithms
    12. Trigonometric ratio
    13. Straight lines
    14. Triangle
    15. Circles
    16. Quadrilateral and parallelogram
    17. Loci and concurrency
    18. Statistics
    19. Rectangular and Cartesian products
    20. Rational expression
    21. Set theory
    22. Factorisation
    23. LCM and HCF
    24. Clocks
    25. Real Analysis
1). If \( \Large \triangle ABC \) is right angled at C, then what is cos (A + B) + Sin (A + B) equal to?
A). 0
B). \( \Large \frac{1}{2} \)
C). 1
D). 2
2). If \( \Large \alpha \), \( \Large \beta \) and \( \Large \gamma \) are acute angled such that \( \Large sin \ \alpha=\frac{\sqrt{3}}{2} \ cos \ \beta=\frac{\sqrt{3}}{2} \) and tan r=1 then what is \( \Large \alpha + \beta + \gamma \) equal to?
A). 105 degree
B). 120 degree
C). 135 degree
D). 150 degree
3). If \( \Large tan \ \theta \) = 3/4 and \( \Large \theta \) is acute, then what is the value of \( \Large sin \ \theta \)?
A). \( \Large -\frac{3}{5} \)
B). \( \Large \frac{3}{5} \)
C). \( \Large \frac{4}{5} \)
D). \( \Large -\frac{4}{5} \)
4). If \( \Large sin \ \theta =\frac{a^{2}-1}{a^{2}+1} \) then the value of \( \Large sec \ \theta + tan \ \theta \) will be
A). \( \Large \frac{a}{\sqrt{2}} \)
B). \( \Large \frac{a}{a^{2}+1} \)
C). \( \Large \sqrt{2}a \)
D). a
5). If \( \Large \alpha + \beta \)=90 degree and \( \Large \alpha : \beta \)=2:1 then the value of \( \Large sin \alpha : sin \beta \) is
A). \( \Large \sqrt{3}:1 \)
B). 2 : 1
C). 1 : 1
D). \( \Large \sqrt{2}:1 \)


6). If \( \Large sin \ \theta + cos \ \theta =1 \), what is the value of \( \Large sin \ \theta \ cos \ \theta \)?
A). 2
B). 0
C). 1
D). 1/2
7). If \( \Large tan \theta \) = 3/4 and \( \Large \theta \) is acute, then \( \Large cosec \theta \) is equal to
A). \( \Large \frac{5}{3} \)
B). \( \Large \frac{5}{4} \)
C). \( \Large \frac{4}{3} \)
D). \( \Large \frac{3}{4} \)
8). The value of \( \Large \left(\frac{1}{(1+tan^{2} \theta )}+\frac{1}{(1+cot^{2} \theta )}\right) \) is
A). 1
B). 2
C). \( \Large \frac{1}{2} \)
D). \( \Large \frac{1}{4} \)
9). The minimum value of \( \Large sin^{2} \theta+cos^{4} \theta \) is
A). \( \Large \frac{1}{\sqrt{2}} \)
B). \( \Large \frac{3}{5} \)
C). \( \Large \frac{3}{4} \)
D). \( \Large \frac{2}{3} \)
10). If \( \Large sec \theta +tan \theta =2 \), what is the value of \( \Large sec \theta \) ?
A). \( \Large \frac{3}{2} \)
B). \( \Large \sqrt{2} \)
C). \( \Large \frac{5}{2} \)
D). \( \Large \frac{5}{4} \)
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