SAT Mathematics - Trigonometry
Exam Duration: 45 Mins Total Questions : 30
If √3 tanθ=3 Sinθ, then value of Sin2θ-Cos2θ is
- (a)
\(\frac{1}{\sqrt{3}}\)
- (b)
\(\frac{1}{\sqrt{2}}\)
- (c)
\(\frac{1}{3}\)
- (d)
\(\frac{1}{4}\)
If sin170=\(\frac{x}{y}\), then the value of Sec170 - Sin730 is
- (a)
\(\frac{y^{2}-x^{2}}{xy}\)
- (b)
\(\frac{x^{2}}{\sqrt{y^{2}-x^{2}}}\)
- (c)
\(\frac{x^{2}}{y\sqrt{y^{2}+x^{2}}}\)
- (d)
\(\frac{x^{2}}{y\sqrt{y^{2}-x^{2}}}\)
If θ
- (a)
0
- (b)
1
- (c)
\(\frac{1}{3}\)
- (d)
\(\frac{1}{\sqrt{3}}\)
The value of sin210+sin250+sin290.....+sin2890 is
- (a)
11\(\frac{1}{2}\)
- (b)
11√2
- (c)
11
- (d)
\(\frac{11}{\sqrt{2}}\)
If cosec 390=x, the value of \(\frac { 1 }{ { cos }^{ 2 }51° } +{ sin }^{ 2 }39°+{ tan }^{ 2 }51°-\frac { 1 }{ { sin }^{ 2 }51°{ sec }^{ 2 }39° } \)is
- (a)
\(\sqrt{x^{2}-1}\)
- (b)
\(\sqrt{1-x^{2}}\)
- (c)
x2-1
- (d)
1-x2
If sinθ+cosecθ=2, then value of sin100θ+cosec100θ is
- (a)
1
- (b)
2
- (c)
3
- (d)
100
If x, y are acute angles, 0<x+y<900 and Siri(2x - 200) = Cos(2y+ 200). value of Tan(x+y) is
- (a)
\(\frac{1}{\sqrt{3}}\)
- (b)
\(\frac{\sqrt{3}}{2}\)
- (c)
√3
- (d)
1
The value of Sin15° is
- (a)
\(\frac{\sqrt{3}+1}{2\sqrt{2}}\)
- (b)
\(\frac{\sqrt{3}-1}{2\sqrt{2}}\)
- (c)
\(\frac{\sqrt{\sqrt{2}-\sqrt{3}}}{2}\)
- (d)
\(\frac{\sqrt{\sqrt{2}+\sqrt{3}}}{2}\)
If φ and θ are complementary angles. then:
- (a)
sinθ=sinφ
- (b)
cosθ=cosφ
- (c)
tanθ=tanφ
- (d)
secθ=cosecφ
If ABC is a triangle then which of the following statements are correct?
I. Sin(A + B) = SinC
II. Sin(\(\frac{A+B}{2}\))=cos\(\frac{C}{2}\)
III. Tan(\(\frac{A+B-C}{2}\))=Cot C
IV. Tan(\(\frac{A-B-C}{2}\))=-CotA
- (a)
I and II
- (b)
I, II and III
- (c)
All of these
- (d)
I,II and IV
Evaluate \(\frac { { sin }^{ 2 }29°+{ sin }^{ 2 }61° }{ { cos }^{ 2 }29°+{ cos }^{ 2 }61° } +\frac { { sin\left( 90°-\theta \right) sin\theta } }{ tan\theta } +\frac { cos\left( 90°-\theta \right) cos\theta }{ cot\theta } \)
- (a)
1
- (b)
0
- (c)
2
- (d)
None of these
Cos4A + Sin4A-2Cos2ASin2A, if CosA= 1
- (a)
0
- (b)
2
- (c)
1
- (d)
none of these
If 3SecA-2CosB =.√3 and B=300 then cos(A-B) is equal to
- (a)
1
- (b)
-1
- (c)
\(\frac{1}{2}\)
- (d)
√3
If cos4θ-sin4θ=\(\frac{2}{3}\) , then the value of 2cos2θ-1 is
- (a)
0
- (b)
1
- (c)
\(\frac{2}{3}\)
- (d)
\(\frac{3}{2}\)
The value of Cot10°.Cot80°.Cot20°.Cot70°.Cot60° is
- (a)
1
- (b)
-2
- (c)
-1
- (d)
√3
If θ be a positive acute angle satisfying cos2θ+cos4θ=1, then the value of tan2θ+tan4θ is
- (a)
\(\frac{3}{2}\)
- (b)
1
- (c)
\(\frac{1}{2}\)
- (d)
0
The value of tan4°.tan 43°. tan 47°. tan 86° is
- (a)
0
- (b)
1
- (c)
√3
- (d)
1/√3
Find the value of 1 + Tan45°. Cot85° is equal to
- (a)
sin25°
- (b)
cos25°
- (c)
sec25°
- (d)
cosec25°
\(\sqrt{\frac{1+sinθ}{1-sinθ}}\) is equal to
- (a)
secθ+tanθ
- (b)
secθ-tanθ
- (c)
tanθ-secθ
- (d)
sec2θ+tan2θ
If A and B are acute angles and SinA= CosB, then A+B is
- (a)
60°
- (b)
90°
- (c)
45°
- (d)
0°
If x=rsinθcosφ, y=r sinθsinφ and z=r cosθ, then x2+y2+z2=
- (a)
r
- (b)
r2
- (c)
\(\frac{r^{2}}{2}\)
- (d)
2r2
What is the maximum value of Tanθ
- (a)
1
- (b)
not defined
- (c)
√3
- (d)
\(\frac{1}{\sqrt{3}}\)
Which of the following is not possible?
- (a)
sinθ=1, cosθ=0
- (b)
sinθ=0, cosθ=1
- (c)
sinθ=\(\frac{\sqrt{3}}{2}\) , cosθ=\(\frac{1}{2}\)
- (d)
sinθ=1, cosθ=\(\frac{1}{\sqrt{2}}\)
If in ΔABC, ㄥB=90°, AB=12cm and BC=5cm, then value of tan A is
- (a)
\(\frac{5}{13}\)
- (b)
\(\frac{5}{12}\)
- (c)
\(\frac{13}{5}\)
- (d)
\(\frac{12}{5}\)
The value of [cos0°-sin(90°-0°)][cos0°+sin(90°-θ°)] is
- (a)
sinθ
- (b)
sin2θ
- (c)
cosθ
- (d)
cos2θ
In any triangle ABS value of sin\((\frac{B+C}{2})\) is
- (a)
cos \(\frac{A}{2}\)
- (b)
sin\(\frac{A}{2}\)
- (c)
-sin\(\frac{A}{2}\)
- (d)
-cos\(\frac{A}{2}\)
The value of \(\frac{sin19°}{cos71°}\)is equal to
- (a)
>1
- (b)
1
- (c)
<1
- (d)
0
If sin∝=cos∝, then the value of ∝ is
- (a)
30°
- (b)
45°
- (c)
60°
- (d)
90°
cos\((\frac{\pi}{2}-30°)\)is equal to
- (a)
\(\frac{1}{\sqrt{3}}\)
- (b)
\(\frac{1}{\sqrt{2}}\)
- (c)
\(\frac{1}{2}\)
- (d)
\(\frac{\sqrt{3}}{2}\)
If cotθ=\(\frac{b}{a}\) , then value of \(\frac{cosθ+sinθ}{cosθ-sinθ}\) is
- (a)
\(\frac{b-a}{b+a}\)
- (b)
b-a
- (c)
b+a
- (d)
\(\frac{b+a}{b-a}\)
