Unit circle Quiz 1

Question 1

Which of these points lie on the unit circle?

Accepted Answer

$$\left( { - \dfrac{{\sqrt 3 }}{2}, - \dfrac{1}{2}} \right)$$

Answer

$$\left( {\dfrac{1}{{\sqrt 2 }},\dfrac{{\sqrt 2 }}{1}} \right)$$

Answer

$$\left( {\dfrac{{\sqrt 3 }}{2},\dfrac{1}{{\sqrt 3 }}} \right)$$

Answer

$$\left( {\dfrac{1}{2},\dfrac{1}{2}} \right)$$

Question 2

If $$\left( { - \dfrac{{\sqrt 3 }}{2}, - \dfrac{1}{2}} \right)$$ is a terminal point of a unit circle then find the angle made line joining the terminal point with x axis.

Accepted Answer

$$\dfrac{{7\pi }}{6}$$

Answer

$$\dfrac{\pi }{6}$$

Answer

$$\dfrac{{5\pi }}{6}$$

Answer

None of these

Question 3

Find the terminal point of the unit circle at $$	heta  = 66^\circ $$.

Accepted Answer

$$\left( {0.4067,0.9135} \right)$$

Answer

$$\left( {0,0.9135} \right)$$

Answer

$$\left( {0.4067,0} \right)$$

Answer

$$\left( { - 0.4067, - 0.9135} \right)$$

Question 4

Identity when the equation of the unit circle is a complex plane.

Accepted Answer

$$\cos 	heta + i\sin 	heta = {e^{i	heta }}$$

Answer

$${x^2} + {y^2} = 1$$

Answer

$${x^2} - {y^2} = 1$$

Answer

$$\cos 	heta - i\sin 	heta = \cos 	heta$$

Question 5

If the equation of the unit circle is $${x^2} + {y^2} = {r^2}$$. What is the value of $$\sec 	heta $$.

Accepted Answer

$$ \pm \dfrac{1}{x}$$

Answer

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

Answer

$$0$$

Answer

$$ \pm y$$