Trigonometric Ratios

Q.

What is the value of $\cos 37$ in fraction?

Q.

If $\left|a\right|=10,\left|b\right|=2anda.b=12,$ then $|a\times b|$ is equal to?

1. $12$

2. $14$

3. $16$

4. $18$

Q. If $cot\theta =\frac{7}{8}$, evaluate:
$\frac{(1+sin\theta )(1-sin\theta )}{(1+cos\theta )(1-cos\theta )}$

1. $\frac{49}{64}$
2. $\frac{49}{8}$
3. $\frac{7}{64}$
4. $\frac{7}{8}$

Q.

Evaluate the value of $\tan 270°$.

Q.

If $y=sec{x}^0$, then $\frac{dy}{dx}=$

1. $sec\left(x\right)\tan \left(x\right)$

2. $sec\left(x^0\right)\tan \left(x^0\right)$

3. $sec\left(x^0\right)\tan \left(x^0\right)\frac{\mathrm{\pi }}{180}$

4. $sec\left(x^0\right)\tan \left(x^0\right)\frac{180}{\mathrm{\pi }}$

Q.

If $\frac{(\cos A)}{3}=\frac{(\cos B)}{4}=\frac{1}{5},-\pi /2<A<0,-\pi /2<B<0$, then the value of $2\sin A+4\sin B$ is

1. $4$

2. $-2$

3. $-4$

4. $0$

Q.

The angle of elevation of a cloud $C$ from a point $P,200m$ above a still lake is ${30}^{°}$. If the angle of depression of the image of $C$ in the lake from the point $P$ is $60°$, then $PC$ (in m) is equal to

1. $200\sqrt{3}$

2. $400\sqrt{3}$

3. $400$

4. $100$

Q.

The value of $\frac{\sin \left(55°\right)-\cos \left(55°\right)}{\sin \left(10°\right)}$ is

1. $\frac{1}{\sqrt{2}}$

2. $2$

3. $1$

4. $\sqrt{2}$

Q.

$ABC$ is a triangular park with $AB=AC=100m$.

A vertical tower is situated at the midpoint of $BC$.

The angle of elevation, if the top of the tower at $AandB$ are $co{t}^{-1}3\sqrt{2}$ and $\cos e{c}^{-1}2\sqrt{2}$, respectively.

The height of the tower is

1. $16$ m

2. $25$ m

3. $50$ m

4. $20$ m

Q.

Find the reference angle for 390 degree

1. 10 degrees

2. 90 degrees

3. 120 degrees

4. 30 degrees

Q.

If A and B are acute angles of a right angled triangle and sinA = cosB, then

1. A - B =

2. A - B =

3. A + B =

4. A + B =

Q.

If sin A = $\frac{8}{17}$, find the value of secA cosA + cosecA cosA.

1. 

2. 

3. 

4. 

Q.

If $\cos A=\cos B\cos C$ and $A+B+C=\pi$, then the value of $cotBcotC$ is

1. $1$

2. $2$

3. $\frac{1}{3}$

4. $\frac{1}{2}$

Q.

What is the trigonometric ratio and its importance ?

Q.

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of $30°$, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be $60°$. Find the time taken by the car to reach the foot of the tower from this point.

Q.

From the top of a hill $h$ meters high, the angles of depressions of the top and the bottom of a pillar are $\alpha$ and $\beta$, respectively. The height (in metres) of the pillar is

1. $h\frac{[tan\beta –tan\alpha ]}{[tan\beta ]}$

2. $h\frac{[\tan \alpha –\tan \beta ]}{[\tan \alpha ]}$

3. $h\frac{[\tan \alpha +\tan \beta ]}{[\tan \beta ]}$

4. $h\frac{[\tan \alpha +\tan \beta ]}{[\tan \alpha ]}$

Q.

If $\sin \left(\theta \right)+\cos \left(\theta \right)=0$ and $0<\theta <\pi$, then $\theta$ is equal to

1. $0$

2. $\frac{\pi }{4}$

3. $\frac{\pi }{2}$

4. $\frac{3\pi }{4}$

Q.

The value of $tan{58}^{\circ }tan{32}^{\circ }tan{57}^{\circ }tan{33}^{\circ }$ is

1. 0

2. 1

3. 3

4. 2

Q.

Find the reference angle for 120 degree

1. 60

2. 80

3. 120

4. 140

Q. Question 5
Given $sec\theta$ = $\frac{13}{12}$, calculate all other trigonometric ratios.

Q. In trapezium ABCD, as shown, AB || DC, AD = DC = BC = 20 cm and ∠A = ${60}^{\circ }$. Find:
(i) length of AB
(ii) distance between AB and DC

Q. if l= m sec theta + n tan theta and k= n sec theta + m tan theta

Q.

The value of $\sin$ 60${}^{\circ }$ is

1. 1

2. 1/2

3. √3/2

4. 1/ √2

Q. A boy standing at a point O finds his kite flying at a point P with distance OP = 25 m. It is at a height of 5 m from the ground. When the thread is extended by 10 m from P, it reaches a point Q. What will be the height QN of the kite from the ground?

1. 5 m
2. 6 m
3. 7 m
4. 8 m

Q.

Find the value of $(\sin 30°+\cos 30°)-(\sin 60°+\cos 60°)$.

Q.

$\Delta ABC$ is right angled at B, given $5\times sinA=3$.
Find cosC+tanA + cosecC.

1. $\frac{12}{5}$

2. $\frac{13}{12}$

3. $\frac{13}{5}$

4. $\frac{12}{5}$

Q.

Using the measurements given in the figure, the value of $tan\theta$ = _________.

1. 2

2. $\frac{3}{4}$

3. $\frac{4}{3}$

4. 1

Q. An angle which measures more than 180° but less than 360° is called
(a) an acute angle
(b) an obtuse angle
(c) a straight angle
(d) a reflex angle

Q. If $sinA:cosA=4:7$, then what is the value of $\frac{7sinA-3cosA}{7sinA+2cosA}$?

1. $\frac{1}{6}$
2. $\frac{2}{12}$
3. $\frac{2}{6}$
4. $\frac{3}{9}$

Q.

In $△ABC,\angle B={90}^{\circ }$ and $sinA=\frac{5}{13}$, then $se{c}^{2}A-ta{n}^{2}A=$ __________________

1. -1

2. 0

3. 1

4. 2