Range of Trigonometric Expressions

Q.

The maximum value of 3cos $\theta$ - 4 sin$\theta$ is

1. 3

2. 4

3. 5

4. None of these

Q.

The maximum value of $5+(sinx-4{)}^2$ is

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Q.

The maximum value of $1+2\sin x+3{\cos }^{2}x$ is

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

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

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

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

Q.

Minimum value of $5si{n}^2\theta +4co{s}^2\theta$ is

1. 1

2. 2

3. 3

4. 4

Q.

If x and y are the maximum and minimum values of sin $\theta$ + cos $\theta$, find the value of $x^2$ + $y^2$

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Q.

The minimum value of $9ta{n}^2\theta +4co{t}^2\theta$ is

1. 13

2. 6

3. 9

4. 12

Q.

Let $f\left(x\right)=cosx(sinx+\sqrt{si{n}^{2}x+si{n}^2\theta }),\theta$ is a given const, then max of f(x)is

1. $\sqrt{1+cs{c}^2\theta }$

2. $\sqrt{1+si{n}^2\theta }$

3. $|cos\theta |$

4. $|sin\theta |$

Q.

The minimum value of $3sin\theta +4cos\theta$ is

1. 5

2. 3

3. -5

4. 1

Q.

The value of a cos $\theta$ + b sin $\theta$ lies between

1. 

2. 

3. a-b and a+b

4. a and b

Q.

$\alpha ,\beta ,\gamma$ are real numbers satisfying $\alpha +\beta +\gamma =\pi$.

The value of the given expression

$sin\alpha +sin\beta +sin\gamma$ is

1. -3

2. Zero

3. Positive

4. Negative