Use of Trigonometric Table

Q.

Show that:$\cos 38°\cos 52°–\sin 38°\sin 52°=0$

Q.

If ${\sin }^{-1}\frac{1}{2}={\tan }^{-1}x$ then $x=$

1. $\sqrt{3}$

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

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

4. None of these

Q.

A flagstaff 6 metres high throws a shadow 2$\sqrt{3}$ m long on the ground. The angle of elevation (in degree) of the top of the flagstaff from the point where the shadow ends.

___

Q. Two persons are standing on the opposite sides of a tower. They observe the angles of elevation of the top of the tower to be ${30}^{\circ }$ and ${38}^{\circ }$ respectively. Find the distance between them, if the height of the tower is 50 m. [2 MARKS]

Q. Question 1 (iv)
Evaluate the following:
(iv) $\frac{(sin{30}^{\circ }+tan{45}^{\circ }-cosec{60}^{\circ })}{(sec{30}^{\circ }+cos{60}^{\circ }+cot{45}^{\circ })}$

Q. Find the area of the right angled triangle with hypotenuse 5 cm and one of the acute angle is 48°30'.
(Refer the trigonometric table for the values)

1. 6.2093525 ${cm}^2$
2. 6.2052935 ${cm}^2$
3. 6.3025925 ${cm}^2$
4. 6.2035925 ${cm}^2$

Q.

Evaluate: $\frac{\text{sin}{30}^{\circ }+\text{tan}{45}^{\circ }-\text{cosec}{60}^{\circ }}{\text{cot}{45}^{\circ }+\text{cos}{60}^{\circ }-\text{sec}{30}^{\circ }}$.

Q. Find the area of a right triangle whose hypotenuse is 10 cm and one of the acute angle is 24°24′. (Given: sin 24° 24′ = 0.4131, cos 24° 24′ = 0.9107)

1. $15c{m}^2$
2. $16.59c{m}^2$
3. $17.57c{m}^2$
4. $18.81c{m}^2$

Q.

$2\sin 45°\cos 45°=1$, how?

Q. Find the value of tan70°13'.
(Refer the trigonometric table for the values)

1. 2.7902
2. 2.7804
3. 3.7802
4. 2.7802

Q.

If $cotA=\frac{12}{5}$, then the value of (sinA+cosA) $\times$ cosecA is:

1. 1

2. 13/5

3. 17/5

4. 14/5

Q.

If $a=30$, then $\frac{{\cos }^{3}a-\cos 3a}{\cos a}+\frac{{\sin }^{3}a+\sin 3a}{\sin a}=$

Q. Question 4 (iv)
State whether the following are true or false. Justify your answer.
(iv) $sin\theta =cos\theta$ for all values of $\theta$.

Q. Find the value of tan16°32'.
(Refer the trigonometric table for the values)

1. 0.2986
2. 0.2869
3. 0.2968
4. 0.9268

Q.

Express as a function of positive acute angles: $\cos \left(240\right)·\sin \left(-110\right)$.

Q. Find the value of sin70°13'.
(Refer the trigonometric table for the values)

1. 0.941
2. 0.9104
3. 0.9401
4. 0.9408

Q. The value of cos69°45' - cos15°40' is .

1. $-$ 0.6168
2. 0.6168
3. $-$ 0.6618
4. 0.6618

Q. Find the value of tan20°15'.
(Refer the trigonometric table for the values)

1. 0.3698
2. 0.3689
3. 0.3965
4. 0.3986

Q. A line drawn from the eye of the observer to the point in the object viewed by the observer is called _____.

1. Angle of elevation
2. Angle of depression
3. Line of sight
4. Horizontal level

Q. Verify: $8\sin 2x\cos 4x\sin 6x$, when $x={15}^0$
$\left[2\right]$

Q. Question 6
The value of $(tan{1}^{\circ },tan{2}^{\circ },tan{3}^{\circ }\dots \dots tan{89}^{\circ })$ is

(A) 0
(B) 1
(C) 2
(D) $\frac{1}{2}$

Q. Find the area of the right angled triangle with hypotenuse 5 cm with one of the acute angle equal to 19°59'.
(Refer the trigonometric table for the values)

1. 4.0155592 ${cm}^2$
2. 4.0152955 ${cm}^2$
3. 4.0152559 ${cm}^2$
4. 4.0192555 ${cm}^2$

Q. Find the value of sin22°14' + cos 75°13'.
(Refer the trigonometric table for the values)

1. -0.6334
2. 0.6334
3. 0.6831
4. -0.6831

Q. Find the value of cos69°45' - cos15°40'.
(Refer the trigonometric table for the values)

1. - 0.6495
2. 0.6495
3. - 0.6618
4. 0.6618

Q.

Evaluate: $\frac{\sin {60}^0}{{\cos }^2{45}^0}-cot{30}^0+15\cos {90}^0$

Q. If tan A = 0.8021, then find the value of A. (Given: tan 38° 42′ = 0.8012, tan 38° 48′ = 0.8040 and mean difference for 2' = 9.)

1. 38°41'
2. 38°42'
3. 38°43'
4. 38°44'

Q. Evaluate: $2\ast \left(\frac{{\cos }^2{20}^0+{\cos }^2{70}^0}{{\sin }^2{25}^0+{\sin }^2{65}^0}\right)-\tan {45}^0+\tan {13}^0\tan {23}^0\tan {30}^0\tan {67}^0\tan {77}^0$.

Q. Find the value of tan29°11'.
(Refer the trigonometric table for the values)

1. 0.5585
2. 0.8555
3. 0.5635
4. 0.6123

Q.

The value of $\frac{cosA}{cotA}+sinA$ is:

1. cotA

2. 2sinA

3. 2cosA

4. secA

Q. The value of ${cosec}^2{51}^0-{cot}^2{51}^0$ is

1. -1
2. 1
3. 0
4. $\frac{1}{2}$