Solving trigonometric equations Quiz 1

Question 1

Find the value of $$x$$ $$($$in the first quadrant$$)$$ if $$\sin \left( \dfrac{29}{5}x \right)=0$$.

Accepted Answer

$${{0}^{\circ }}$$

Answer

$${{30}^{\circ }}$$

Answer

$${{60}^{\circ }}$$

Answer

$${{210}^{\circ }}$$

Question 2

Solve the equation $$	an \dfrac{13y}{5}=1$$.

Accepted Answer

$$y=\dfrac{5\pi }{52}$$

Answer

$$y=\dfrac{3\pi }{17}$$

Answer

$$y=\dfrac{4\pi }{29}$$

Answer

$$y=\dfrac{6\pi }{19}$$

Question 3

If  $$\cot \dfrac{9	heta }{5}=\left( {{\sin }^{2}}	heta +{{\cos }^{2}}	heta  ight)$$, then the write the value of $$	heta $$.

Accepted Answer

$$\dfrac{5\pi }{36}$$

Answer

$$\dfrac{4\pi }{17}$$

Answer

$$\dfrac{3\pi }{19}$$

Answer

$$\dfrac{8\pi }{27}$$

Question 4

For which of the following values of $$'t'$$ the equation $$\cos \left( 9t+1 ight)={{\sec }^{2}}\dfrac{t}{2}-{{	an }^{2}}\dfrac{t}{2}$$ is true?

Accepted Answer

$$-\dfrac{1}{9}$$

Answer

$$\dfrac{1}{2}$$

Answer

$$1$$

Answer

$$0$$

Question 5

$$\dfrac{\cos \left( \dfrac{15g}{77} \right)+\sin \left( \dfrac{15g}{77} \right)}{\cos \left( \dfrac{15g}{77} \right)-\sin \left( \dfrac{15g}{77} \right)}=-1$$, then solve the equation and write the value of $$g$$.

Accepted Answer

$$0$$

Answer

$$1$$

Answer

$$\dfrac{1}{2}$$

Answer

$$\dfrac{1}{3}$$