Trigonometry basics Quiz 1

Question 1

If $$sec	heta +tan	heta =a$$, then what is the value of $$tan	heta $$ in terms of $$a$$?

Accepted Answer

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

Answer

$$\dfrac{1+{{a}^{2}}}{2a}$$

Answer

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

Answer

$$\dfrac{2{{a}^{2}}+1}{2a}$$

Question 2

If $$tanA=\sqrt{2}$$ then what is the value of $$sinA$$ and $$sin2A$$ ?

Accepted Answer

$${\dfrac{1}{\sqrt{3}}}$$ and $$\sqrt{\dfrac{2}{3}}$$

Answer

$$\dfrac{\sqrt{2}}{3}$$ and $$2\sqrt{\dfrac{2}{3}}$$

Answer

$$\sqrt{\dfrac{2}{3}}$$ and $$2\dfrac{\sqrt{2}}{3}$$

Answer

$${\dfrac{2}{\sqrt3}}$$ and $$2{\dfrac{2}{\sqrt3}}$$

Question 3

Given $$10cos^{2}x-4\sqrt{10}cosx+4=0$$, then find the value of $$ta{{n}^{2}}x$$.

Accepted Answer

$$\dfrac{3}{2}$$

Answer

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

Answer

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

Answer

$$\dfrac{9}{4}$$

Question 4

If $$sin^{120}x+cos^{120}x=1$$, and $$x$$ is in the range of $$[-4\pi ,7\pi ]$$ , how many values can $$x$$ take?

Accepted Answer

23

Answer

22

Answer

12

Answer

20

Question 5

If $$cosec(y) cot(y)=\lambda $$, then find the value of $$sin\left( \dfrac{y}{2} \right)$$.

Accepted Answer

$$\dfrac{\pm \lambda }{\sqrt{(1+{{\lambda }^{2}})}}$$

Answer

$$\dfrac{\lambda }{\sqrt{(1+{{\lambda }^{2}})}}$$

Answer

$$\dfrac{-\lambda }{\sqrt{(1+{{\lambda }^{2}})}}$$

Answer

$$\dfrac{2\lambda }{\sqrt{(1+{{\lambda }^{2}})}}$$