A question on trigonometry!

Find the number of solutions of the equation given below,

$\sqrt{3}\sin \theta+ \cos \theta = 4$

#Geometry

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

For real solutions? Answer is 0.

Just apply the Trigonometric R method.

Pi Han Goh - 5 years, 5 months ago

Thank you very much!

Akshay Yadav - 5 years, 5 months ago

No, this is the quickest method. $\quad\quad \quad$

Pi Han Goh - 5 years, 5 months ago

Since the maximum real value for $\sin \theta$ and $\cos \theta$ is $1$ , LHS cannot be larger than $\sqrt{3}+1 < 4$ , therefore, there is no real root.

Chew-Seong Cheong - 5 years, 5 months ago

Thanks! I also used the same method to solve the question in exam and wondering if it was correct or not.

Akshay Yadav - 5 years, 5 months ago

Your method is right, but the maximum value of LHS is not $\sqrt3+1$ .

Aditya Agarwal - 5 years, 5 months ago

I did not say that the maximum value is $\sqrt{3}+1$ . What I meant was LHS $\ne$ RHS.

Chew-Seong Cheong - 5 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$