Trigonometric ratios - class-IX

Question 1 Multiple Choice (Single Answer)

$\sin ^{ 8 }{ \theta } -\cos ^{ 8 }{ \theta } -\left( \sin ^{ 2 }{ \theta } -\cos ^{ 2 }{ \theta } \right) \left( 1-\sin ^{ 2 }{ \theta } \right) $=0

True
False

Question 2 Multiple Choice (Single Answer)

If $tan x + cot x = 2$, then $sin^{2n}x+cos^{2n}x=$

$\dfrac{1}{2}$
$2^n$
$\dfrac{1}{2^n}$
$\dfrac{1}{2^{n-1}}$

Question 3 Multiple Choice (Single Answer)

If $\tan x =\dfrac{3}{4} , \pi < x < \dfrac{3\pi}{2} $ find value of $\sin\dfrac{x}{2} , \cos\dfrac{x}{2} , \tan \dfrac{x}{2}$

cos x/2= 3/2, sin x/2 =-3/2, tan x/2= -1/√10
cos x/2= 3/√10, sin x/2 =-3/2, tan x/2= -1/√10
cos x/2= -1/√10, sin x/2 = 3/√10, tan x/2= -3
cos x/2= 3/√10, sin x/2 =-2/3, tan x/2= -1/√10

Question 4 Multiple Choice (Single Answer)

If $\tan \theta+\left(\dfrac {\pi}{2}+\theta\right)=0$ then the most general value of $\theta$ is (where $n\ \in\ Z$)

$n\ \pi \pm \dfrac {\pi}{4}$
$2n\ \pi \pm \dfrac {\pi}{4}$
$2n\ \pi \pm \dfrac {\pi}{4}$
$\dfrac {n\pi}{2}+(-1)^{n} ,\dfrac {\pi}{4}$

Question 5 Multiple Choice (Single Answer)

$\sin\ (45^{o}+\theta)-\cos\ (45^{o}-\theta)$ is equal to

$2\cos \theta$
$0$
$2\sin \theta$
$1$

Question 6 Multiple Choice (Single Answer)

What is the exact value of $cos \theta$ trigonometric functions for the angle formed when the terminal side passes through $(6, 8)$?

$\dfrac{3}{5}$
$\dfrac{6}{5}$
$\dfrac{4}{5}$
$\dfrac{8}{5}$

Question 7 Multiple Choice (Single Answer)

Determine the exact value of $\cos \theta$ trigonometric functions for the angle formed when the terminal side passes through $(3, 4).$

$\dfrac{4}{5}$
$\dfrac{3}{5}$
$\dfrac{2}{5}$
$\dfrac{1}{5}$

Question 8 Multiple Choice (Single Answer)

Let $\theta$ be an angle in standard position with (x, y) a point on the terminal side of $\theta$ and r = $\sqrt{x^{2}+y^{2}}\neq 0$. What is cos $\theta$?

$\dfrac{y}{r}$
$\dfrac{r}{y}$
$\dfrac{x}{r}$
$\dfrac{r}{h}$

Question 9 Multiple Choice (Single Answer)

Find the exact value of sec $\theta$ trigonometric functions for the angle formed when the terminal side passes through (3, 4).

$\dfrac{4}{5}$
$\dfrac{3}{5}$
$\dfrac{2}{5}$
$\dfrac{5}{4}$

Question 10 Multiple Choice (Single Answer)

Find sec $\theta$, if $\theta$ be an angle in standard position with (x, y) a point on the terminal side of $\theta$ and r = $\sqrt{x^{2}+y^{2}}\neq 0$.

$\dfrac{y}{r}$
$\dfrac{r}{y}$
$\dfrac{x}{r}$
$\dfrac{r}{x}$

Question 11 Multiple Choice (Single Answer)

Find the exact value of sin $\theta$ trigonometric functions for the angle formed when the terminal side passes through (6, 8).

$\dfrac{4}{5}$
$\dfrac{6}{5}$
$\dfrac{10}{5}$
$\dfrac{3}{5}$

Question 12 Multiple Choice (Single Answer)

Find the exact value of cosec $\theta$ trigonometric functions for the angle formed when the terminal side passes through $(3, 4).$

$\dfrac{4}{5}$
$\dfrac{3}{5}$
$\dfrac{5}{3}$
$\dfrac{5}{4}$

Question 13 Multiple Choice (Single Answer)

Find cot $\theta$, if $\theta$ be an angle in standard position with (x, y) a point on the terminal side of $\theta$ and r = $\sqrt{x^{2}+y^{2}}\neq 0$.

$\dfrac{y}{r}$
$\dfrac{x}{y}$
$\dfrac{x}{r}$
$\dfrac{r}{x}$

Question 14 Multiple Choice (Single Answer)

Find cosec $\theta$, if $\theta$ be an angle in standard position with (x, y) a point on the terminal side of $\theta$ and r = $\sqrt{x^{2}+y^{2}}\neq 0$.

$\dfrac{y}{r}$
$\dfrac{r}{y}$
$\dfrac{x}{r}$
$\dfrac{r}{x}$

Question 15 Multiple Choice (Single Answer)

lf the distance between the points $(a \cos\theta, a \sin\theta), (a \cos\phi, a \mathrm{sin} \phi)$ is $2\mathrm{a}$ then $\theta=$.

$2n\pi\pm\pi+\phi, n\in z$
$n\displaystyle \pi\pm\frac{\pi}{2}+\phi, n\in z$
$n\pi-\phi, n\in z$
$2n\pi+\phi, n\in z$

Question 16 Multiple Choice (Single Answer)

Find the exact value of $\dfrac{\sin \theta}{\sec \theta}$ trigonometric functions for the angle formed when the terminal side passes through $(3, 4)$.

$\dfrac{25}{12}$
$\dfrac{12}{5}$
$\dfrac{12}{25}$
$\dfrac{5}{4}$

Trigonometric ratios - class-IX

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