Question
Find the trigonometric functions of $: – 225^\circ$
✓
Answer
Angle of measure $\left(-225^{\circ}\right)$ : Let $m \angle X O A=-225^{\circ}$ Its terminal arm (ray $O A$ ) intersects the standard unit circle at $P(x, y)$. Draw seg PM perpendicular to the X-axis. $\triangle O M P$ is a $45^{\circ}-45^{\circ}-90^{\circ}$ triangle. $\mathrm{OP}=1$, Since point $P$ lies in the $2$ nd quadrant, $x<0, y>0$
$ \therefore \quad x=-\mathrm{OM}=\frac{-1}{\sqrt{2}} \text { and } y=\mathrm{PM}=\frac{1}{\sqrt{2}}$
$\therefore \quad \mathrm{P} \equiv\left(\frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$
$\sin \left(-225^{\circ}\right)=y=\frac{1}{\sqrt{2}}$
$\cos \left(-225^{\circ}\right)=x=-\frac{1}{\sqrt{2}}$
$\tan \left(-225^{\circ}\right)=\frac{y}{x}=\frac{\frac{1}{\sqrt{2}}}{-\frac{1}{\sqrt{2}}}=-1$
$\operatorname{cosec}\left(-225^{\circ}\right)=\frac{1}{y}=\frac{1}{\left(\frac{1}{\sqrt{2}}\right)}=\sqrt{2}$
$\sec \left(-225^{\circ}\right)=\frac{1}{x}=\frac{1}{\left(-\frac{1}{\sqrt{2}}\right)}=-\sqrt{2}$
$\cot \left(-225^{\circ}\right)=\frac{x}{y}=\frac{1}{\frac{1}{\sqrt{2}}}=-1$
$\frac{\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.
Explore more
Similar questions
A family has two children. One of them is chosen at random and found that the child is a girl. Find the probability that
(i) both the children are girls.
ii. both the children are girls given that at least one of them is a girl.
A box contains 2 blue and 3 pink balls and another box contains 4 blue and 5 pink balls. One ball is drawn at random from one of the two boxes and it is found to be pink. Find the probability that it was drawn from (i) first box. (ii)second box
The equation of one side of an equilateral triangle is $x - y = 0$ and one vertex is $(2+\sqrt3,5).$ Prove that a second side is $\text{y}+(2-\sqrt{3})\text{x}=6$ and find the equation of the third side.f
→Find the equation of the circle, if the equations of two diameters are $2x + y = 6$ and $3x + 2y = 4$ and radius is $9.$
→Find the eccentricity, coordinates of foci, length of the latus-rectum of the following ellipes:
$4\text{x}^2+9\text{y}^2=1$
→$4\text{x}^2+9\text{y}^2=1$
Find the number of words formed by permuting all the letters of the following words:
SERIES.
SERIES.
Solve the following equations:
$\sin\text{x}+\cos\text{x}=\sqrt{2}$
→$\sin\text{x}+\cos\text{x}=\sqrt{2}$
For any two sets A and B, prove that: A' - B' = B - A.
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when
1. $n = 10$
2. $n = 15$
3. $n = 12$
4. $n = 8$
→1. $n = 10$
2. $n = 15$
3. $n = 12$
4. $n = 8$
A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?