Trigonometric ratios Quiz 1

Question 1

Evaluate the value of the expression: $$3\left( {{\sin }^{4}}\left( {{270}^{\circ }}-w \right)+{{\sin }^{4}}\left( {{540}^{\circ }}+w \right) \right)-2\left( {{\sin }^{6}}\left( {{90}^{\circ }}+w \right)+{{\sin }^{6}}\left( {{900}^{\circ }}-w \right) \right)$$.

Accepted Answer

1

Answer

3

Answer

$$\sin 6w+\cos 4w$$

Answer

0

Question 2

Estimate the values of the following $$\sin (.375\pi )$$ and $$\cos (.375\pi )$$.

Accepted Answer

$$\dfrac{\sqrt{2+\sqrt{2}}}{2}$$ and $$\dfrac{\sqrt{2-\sqrt{2}}}{2}$$

Answer

$$\dfrac{\sqrt{2-\sqrt{2}}}{2}$$ and $$\dfrac{\sqrt{2+\sqrt{2}}}{2}$$

Answer

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

Answer

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

Question 3

Determine the nature of the roots of the equation $$2{{\cos }^{2}}\left( \dfrac{h}{2} \right)\sin 2h={{h}^{2}}+{{h}^{-2}},h\le {{20}^{\circ }}$$.

Accepted Answer

No real solution

Answer

More than one real solution

Answer

One real solution

Answer

None of the above

Question 4

Suppose $$3d+4e,4d+3e,5d+5e$$ are the three sides of a triangle, in which $$d,e > 0$$ then determine the nature of the triangle.

Accepted Answer

Obtuse angled triangle

Answer

Right angled triangle

Answer

Equilateral triangle

Answer

None of the above

Question 5

Suppose $$m=\sqrt{{{j}^{2}}{{\cos }^{2}}z+{{k}^{2}}{{\sin }^{2}}z}+\sqrt{{{j}^{2}}{{\sin }^{2}}z+{{k}^{2}}{{\cos }^{2}}z}$$ then determine the difference of maximum and minimum values of $${{m}^{2}}$$.

Accepted Answer

$${{(j-k)}^{2}}$$

Answer

$$2({{j}^{2}}+{{k}^{2}})$$

Answer

$${{(j+k)}^{2}}$$

Answer

$$2\sqrt{{{j}^{2}}+{{k}^{2}}}$$