Trigonometry — Quiz 4

Questions in this quiz (6)

1. A person standing 600 feet away from a lighthouse observes the top of the lighthouse with an angle of elevation of $$55^\circ$$. What is the approximate height of the lighthouse in feet?

   • 856.8
   • 600.0
   • 950.2
   • 760.7

2. Which of the following expressions is equivalent to $$\frac{\cos^4x+\cos^2x\sin^2x}{\sin^2x}$$?

   • $$\cos^2x \csc^2x$$
   • $$\cos^2x \sin^2x$$
   • $$\cos^2x \tan^2x$$
   • $$\cos^4x \sin^2x$$

3. What is the range of the function defined by $$y=4\sin(2x)$$ in the standard $$(x,y)$$ coordinate plane?

   • $$-8 \leq y \leq 8$$
   • $$-4 \leq y \leq 4$$
   • $$-2 \leq y \leq 2$$
   • $$0 \leq y \leq 4$$

4. Line $$BD$$ is a diagonal of square $$WXYZ$$. What is the cosine of angle $$BDX$$?

   • $$\frac{\sqrt{3}}{2}$$
   • $$\frac{\sqrt{2}}{2}$$
   • $$\frac{1}{2}$$
   • $$\sqrt{2}$$

5. Given $$15 \cot A = 8$$, find $$\sec A$$.

   • $$\frac{15}{17}$$
   • $$\frac{17}{15}$$
   • $$\frac{17}{8}$$
   • $$\frac{15}{8}$$

6. In triangle $$ABC$$, right-angled at $$B$$, if $$\tan A = \frac{1}{\sqrt{3}}$$, find the value of: $$\cos A \cos C - \sin A \sin C$$

   • 1
   • $$\frac{1}{2}$$
   • $$\frac{\sqrt{3}}{2}$$
   • 0