Trigonometry — Quiz 3

Questions in this quiz (7)

1. If $$0^\circ \leq x \leq 180^\circ$$ and $$3 \sin(2x) = 1$$, then what is the value of $$x$$?

   • $$10^\circ$$ or $$90^\circ$$
   • $$19.4^\circ$$ or $$160.6^\circ$$
   • $$9.7^\circ$$ or $$80.3^\circ$$
   • $$40.15^\circ$$ or $$4.85^\circ$$

2. If $$\tan^2 \theta = 7$$, what is $$\sec^2 \theta$$?

   • $$12$$
   • $$6$$
   • $$8$$
   • $$\sqrt{15}$$

3. If $$\sin \theta = \frac{3}{5}$$, what is $$\sec^2 \theta - \tan^2 \theta$$?

   • $$\cos^2 \theta$$
   • $$\cos \theta$$
   • $$\sin \theta$$
   • $$1$$

4. If $$0^\circ$$ < $$\theta$$ < $$90^\circ$$ and $$\tan \theta = \frac{4}{3}$$, what is $$\sin \theta + \cos \theta$$?

   • $$\frac{7}{5}$$
   • $$\frac{3}{5}$$
   • $$\frac{4}{5}$$
   • $$\frac{1}{5}$$

5. If it is 12 miles from Town A to Town B, 28 miles from Town A to Town C, and 35 miles from Town B to Town C, which expression gives the angle between the path from Town A to Town B and the path from Town A to Town C?

   • $$\arccos \left( \frac{12^2 + 28^2 - 35^2}{2 \cdot 12 \cdot 28} \right)$$
   • $$28^\circ$$
   • $$\arccos \left(\frac{28^2 + 35^2 - 12^2}{2 \cdot 28 \cdot 35} \right)$$
   • $$38^\circ$$

6. Which of these is equivalent to: $$\frac{\cos^2(x)}{\tan^2(x)}$$?

   • $$\frac{\sin^4(x)}{\cos^2(x)}$$
   • $$\frac{\cos^4(x)}{\sin^2(x)}$$
   • $$\frac{\cos^2(x)}{\sin^2(x)}$$
   • $$\frac{\cos^4(x)}{\tan^2(x)}$$

7. In a right triangle XYZ with angle $$Z=90^\circ$$, $$\sin(X)=\frac{99}{101}$$. What is $$\sin(Y)$$?

   • $$\frac{1}{101}$$
   • $$\frac{20}{101}$$
   • $$\frac{10}{101}$$
   • $$\frac{98}{101}$$