Standard Values

Q. The value of $\theta ,if2cos3\theta =1$ is

1. 
2. 
3. 
4. 

Q.

The value of sin ${90}^{\circ }$ and cos $0^{\circ }$ are:

1. 1, 0

2. 0, 0

3. 0, 1

4. 1, 1

Q.

If the angles of a triangle are in the ratio $1:1:4$, then the ratio of the perimeter of the triangle to its largest side is:

1. $\sqrt{2}+2:3$

2. $3:2$

3. $\sqrt{3}+2:\sqrt{2}$

4. $\sqrt{3}+2:\sqrt{3}$

Q. What is the value of $tan\theta$ in $△$ABC, if $\theta$ is increased by ${30}^{\circ }$.

1. $\sqrt{3}$
2. $\frac{1}{\sqrt{3}}$
3. 0
4. Not defined.

Q.

If a triangle has angles ${45}^{\circ },{45}^{\circ }$, and ${90}^{\circ }$, what is the ratio of the sides of the triangle opposite to these angles respectively?

Q.

If sin B = 1, find the value of B if $0\le B\le 90$.

1. 90

2. 0

3. 45

4. 60

Q.

$△$ ABC, right angled at B, $\angle$ACB = ${60}^{\circ }$, expressions for sec 60 and cosec 60 is

1. AC/BC , AC/AB

2. AC/BC , AC/BC

3. AC/AB , AC/AB

4. AC/AB , AC/BC

Q. In a trapezium ABCD, $AB\parallel DC$ and $DC=2AB$. EFdrawn parallel to AB cuts AD in F and BC in E such that $\frac{BE}{EC}=\frac{3}{4}$ . Diagonal DB intersects $EF$ at $G$, then

1. $5FE=10AB$ is true
2. $7FE=10AB$ is true
3. $5FE=5AB$ is true
4. $3FE=10AB$ is true

Q. The value of $cosec{30}^{\circ }+cot{45}^{\circ }$ is

1. 1
2. 3
3. 4
4. 2

Q.

Given $tan(A+B)=\sqrt{3}$ and $tan(A-B)=\frac{1}{\sqrt{3}}$

If $B<A<{90}^{\circ }$, then,
A (in degrees) = ___
B (in degrees) = ___

Q.

In $△$ABC, $\angle B={90}^{\circ }$.

If $tanA=\frac{1}{\sqrt{3}}$, then

$sinA.cosC+cosA.sinC=$ ___
and, $cosA.cosC-sinA.sinC=$ ___

Q. If the value of $2sin2\theta =\sqrt{3}$, then the value of $\theta$ is ______.

1. ${45}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${90}^{\circ }$

Q.

If cos B = 1, find the value of B if $0\le B\le 90$.

1. 60

2. 45

3. 90

4. 0

Q. In a $\Delta$ABC, $\angle$BAC $={90}^o$, AD is its bisector. If DE$\perp$AC, then DE$\times$ (AB$+$AC)$=$2AB$\times$AC.

1. True
2. False

Q.

In an equilateral triangle ABC , match the following ratios to the values

$$\begin{array}{cc}Trignometricratios& Values\\ \left(i\right)tan{60}^{\circ }& \left(a\right)\frac{1}{\sqrt{3}}\\ \left(ii\right)cot{30}^{\circ }& \left(b\right)\sqrt{3}\\ \left(iii\right)cosec{30}^{\circ }& \left(c\right)2\\ \left(iv\right)sec{30}^{\circ }& \left(d\right)\frac{2}{\sqrt{3}}\end{array}$$

1. (i) –a , (ii) – b , (iii) – a , (iv) – d

2. (i) –b , (ii) – b , (iii) – c , (iv) – d

3. (i) –a , (ii) – b , (iii) – c , (iv) – d

4. (i) –a , (ii) – b , (iii) – c , (iv) – b

Q. If $\sin A=\cos {33}^{\circ }$ find $A$

Q. In the figure below $PQ\parallel AB$, $CQ=4.8$ cm, $QB=3.6$ cm and $AB=6.3$ cm. Find $PQ$.

1. $3.6$ cm
2. $5.6$ cm
3. $4.6$ cm
4. $3.9$ cm

Q. ABC is a right angled triangle.
If $\alpha ={30}^{\circ }$ and AC = 10 cm then find the length of side BC in cm.

1. 5

Q. If $sin\theta +cos\theta =\sqrt{2}sin(90-\theta )$. Find $cot\theta$

Q. In $△$ABC, $\angle B={90}^{\circ }$.

If $tanA=\frac{1}{\sqrt{3}}$, then

$sinA.cosC+cosA.sinC$ = ___