Find the principal solutions of =1 2 . - Vidyadip

Question

Find the principal solutions of $\sin \theta=\frac{1}{\sqrt{2}}$.

✓

Answer

As $\sin \frac{\pi}{4}=\frac{1}{\sqrt{2}}$ and $0 \leq \frac{\pi}{4}<2 \pi, \frac{\pi}{4}$ is a principal solution.
By allied angle formula, $\sin \theta=\sin (\pi-\theta)$.
$
\therefore \sin \frac{\pi}{4}=\sin \left(\pi-\frac{\pi}{4}\right)=\sin \frac{3 \pi}{4} \text { and } 0 \leq \frac{3 \pi}{4}<2 \pi
$
$\therefore \frac{3 \pi}{4}$ is also a principal solution.
$\therefore \frac{\pi}{4}$ and $\frac{3 \pi}{4}$ are the principal solutions of $\sin \theta=\frac{1}{\sqrt{2}}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If $R$ is a symmetric relation on a set A, then write a relation between $R$ and $R^{-1}$.

Diffrentiate the following w.r.t.x

$\log \left[\sec \left( e ^{\times 2}\right)\right]$

$A$ matrix $A$ of order $3 \times 3$ has determinant $5$. What is the value of $|3A|$?

If $\vec{\text{a}}=3\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}},$ then find $\big(\vec{\text{a}}\times\vec{\text{b}}\big)\vec{\text{a}}.$

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors of magnitudes 3 and $\frac{\sqrt{2}}{3}$ repectively such that $\vec{\text{a}}\times\vec{\text{b}}$ is a unit vector. write the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$

Show that following points are collinear $P(4, 5, 2), Q(3, 2, 4), R(5, 8, 0)$

Evaluate the following:
$\tan\Big(\cos^{-1}\frac{8}{17}\Big)$

Write $A^{-1}$ for $\text{A}=\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}$

Obtain the simple logical expression of the following. $[p (∨ (~q) ∨ ~r)] ∧ (p ∨ (q ∧ r)$

Show that function $f(x)=\tan x$ is increasing in $\left(0, \frac{\pi}{2}\right)$