Sign of Trigonometric Ratios in Different Quadrants

Q. If $\sin \theta =-\frac{1}{\sqrt{2}}$ and $\tan \theta =1,$ then $\theta$ lies in the quadrant.

1. first
2. second
3. third
4. fourth

Q. If sin θ =-4/5 and θ lies in 3rd quadrant then cos theta/2 = Options:-1/sqrt5

Q. Find the values of the following trigonometric ratios:
(i) $\sin \frac{5\mathrm{\pi }}{3}$

(ii) sin 17π

(iii) $\tan \frac{11\mathrm{\pi }}{6}$

(iv) $\cos \left(-\frac{25\mathrm{\pi }}{4}\right)$

(v) $\tan \frac{7\pi }{4}$

(vi) $\sin \frac{17\pi }{6}$

(vii) $\cos \frac{19\pi }{6}$

(viii) $\sin \left(-\frac{11\pi }{6}\right)$

(ix) $\mathrm{cosec}\left(-\frac{20\pi }{3}\right)$

(x) $\tan \left(-\frac{13\pi }{4}\right)$

(xi) $\cos \frac{19\pi }{4}$

(xii) $\sin \frac{41\pi }{4}$

(xiii) $\cos \frac{39\pi }{4}$

(xiv) $\sin \frac{151\pi }{6}$

Q. If sin x + cos x = 0 and x lies in the fourth quadrant, find sin x and cos x.

Q.

If sin $\theta$ = $-\frac{1}{\sqrt{2}}$ and tan $\theta$ = 1, then $\theta$ lies in which quadrant.

1. First

2. Third

3. Fourth

4. Second

Q.

Find sin $\frac{x}{2}$, cos $\frac{x}{2}$ and tan $\frac{x}{2}$ in each of the following:

tan x = - $\frac{4}{3}$, x in quadrant II.

Q. Range of $f\left(x\right)=\frac{tan\left(\pi \right[x^2-x\left]\right)}{1+sin\left(cosx\right)}$ is (where [x] denotes the greatest integer function

1. 
2. 
3. [tan 2, tan 1]
4. {0}

Q.

In the third quadrant the value of the sine function

1. increases from 0 to 1

2. decreases from 1 to 0

3. decreases from 0 to -1

4. increases from -1 to 0

Q.

Find the value of $sin{210}^{\circ }+cos{120}^{\circ }+tan{225}^{\circ }+cot{315}^{\circ }+sec{300}^{\circ }+cosec{150}^{\circ }$.

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Q.

Find sin $\frac{x}{2}$, cos $\frac{x}{2}$ and tan $\frac{x}{2}$ in the following:

cos x = $\frac{-1}{3}$, x in quadrant III.

Q.

If sin $\theta =\frac{3}{5}$ and cos $\varphi =\frac{-12}{13}$ where $\theta$and $\varphi$ both lie in the second quadrant, find the values of

(i) sin $(\theta -\varphi )$, (ii) cos $(\theta +\varphi )$, (iii) tan $(\theta -\varphi )$.

Q. Find the value of $tan{1}^{\circ }tan{2}^{\circ }tan{3}^{\circ },................tan{89}^{\circ }$.
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Q.

Prove that $\frac{\text{sin}(x+y)}{\text{sin}(x-y)}=\frac{\text{tan}x+\text{tan}y}{\text{tan}x-\text{tan}y}$

Q.

If x lies in third quadrant and 5 sin x + 3 = 0, find the value of

$\frac{2tanx-5sinx+cotx}{2sin\frac{x}{2}cos\frac{x}{2}}$

Q.

If $cosA=\frac{4}{5}$ and $cosB=\frac{12}{13},\frac{3\pi }{2}<A,B<2\pi$, find the value of the following

$\left(i\right)cos(A+b)$

$\left(ii\right)sin(A-B)$

Q.

If A + B = $\frac{\pi }{4}$ where A, B $\in R^{+}$, then the minimum value of (1+tanA) (1+tanB) is always equal to

1. 2

2. 4

3. 1

4. 0

Q.

If sin A = $\frac{4}{5}$ and cos B = - $\frac{12}{13}$, where A and b lie in first

and third quadrant respectively, then cos(A + B) =

1. 

2. 

3. 

4. 

Q.

What trigonometric ratios give negative values in III quadrant?

1. A.tan & cot

2. B.sin & cosec

3. C.cos & sec

4. Both B & C

5. Both A& B

Q.

What is the value of sin x if sec x = 13/5, and x lies in fourth quadrant.

1. 

2. 

3. 

4. 

Q.

What is the sign of the sinA and tanA in third quadrant respectively

1. negative and positive

2. negative and negative.

3. positive and positive

4. positive and negative

Q. If $\cos A=-\frac{12}{13}\mathrm{and}\cot B=\frac{24}{7}$, where A lies in the second quadrant and B in the third quadrant, find the values of the following:

(i) sin (A + B)
(ii) cos (A + B)
(iii) tan (A + B)

Q. The value of ${\sin }^{2}6{}^{\circ }+{\sin }^{2}12{}^{\circ }+{\sin }^{2}18{}^{\circ }+\cdots +{\sin }^{2}84{}^{\circ }+{\sin }^{2}90{}^{\circ }$
is

1. $0$
2. $7$
3. $8$
4. $9$

Q. If $\cos \theta =-\frac{7}{25}$ and $\pi <\theta <\frac{3\pi }{2}$, then $\tan \theta$ is equal to

1. $-\frac{25}{7}$
2. $\frac{25}{7}$
3. $-\frac{24}{7}$
4. $\frac{24}{7}$

Q. $\frac{\tan \left(\frac{35\pi }{6}\right).\sin \left(\frac{11\pi }{3}\right).\sec \left(\frac{7\pi }{3}\right)}{\cot \left(\frac{5\pi }{4}\right).cosec\left(\frac{7\pi }{4}\right).\cos \left(\frac{17\pi }{6}\right)}=$

1. $\sqrt{\frac{2}{3}}$
2. $-\sqrt{\frac{2}{3}}$
3. $\sqrt{\frac{3}{2}}$
4. $\frac{\sqrt{3}}{2}$

Q. If $\tan \theta =-\frac{1}{\sqrt{3}},$ then the value of $\theta \in [0,2\pi ]$ for which $\frac{\cos \theta -{\cos }^3\theta }{\tan \theta +2}$ is always positive is

1. $\frac{4\pi }{3}$
2. $-\frac{\pi }{6}$
3. $\frac{\pi }{6}$
4. $\frac{11\pi }{6}$

Q.

Convert the complex numbers in to the polar form:

-i +i

Q.

Find the value of ${\sin }^n{1890}^{\circ }+{\text{cosec}}^n{1890}^{\circ }$. Where $n\in N$

1. $n$

2. $2n$

3. $1$

4. $2$

Q. If $x\in (\frac{-\pi }{2},\frac{\pi }{2}),$ then $\sqrt{\frac{1-\sin x}{1+\sin x}}$ is equal to

1. $\sec x-\tan x$
2. $\sec x+\tan x$
3. $\tan x-\sec x$
4. $-\tan x-\sec x$

Q. The value of tan(–945°) is

tan(–945°) का मान है

1. –1
2. –2
3. –3
4. –4

Q. Match the following range of angles in which the given trigonometric ratios are positive.

1. $\sin \theta ,\cos ec\theta$
2. $\cos \theta ,sec\theta$
3. $\tan \theta ,cot\theta$
4. All of them