Trigonometry — Quiz 6

Questions in this quiz (8)

1. A person is launching a ball to reach the top of a flagpole. The person stands 40 meters away from the base of the flagpole and releases the ball from a height of 1 meter above the ground. The flagpole is 120 meters tall. At what angle should the ball be launched relative to the ground to hit the top of the flagpole?

   • $$\frac{119}{40}$$
   • $$\cos^{-1}\left(\frac{40}{119}\right)$$
   • $$\tan^{-1}\left(\frac{119}{40}\right)$$
   • $$\sin^{-1}\left(\frac{119}{125}\right)$$

2. Which of the following expressions is equivalent to:$$\frac{\sin^2x}{\csc^2x}-\tan^2x\sin^2x$$

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

3. Given that $$\beta$$ is measured in radians and $$3\cos^2\beta - 4\cos\beta = 1$$ for 0 < $$\beta$$ < $$\frac{\pi}{2}$$, what is the value of $$\sin\beta$$?

   • $$\frac{\sqrt{2}}{2}$$
   • $$\frac{\sqrt{3}}{2}$$
   • $$\frac{\sqrt{-2+4\sqrt{7}}}{3}$$
   • $$\frac{2\sqrt{3}}{3}$$

4. If $$\sin 3A = \cos(A - 26^\circ)$$, where $$3A$$ is an acute angle, find the value of $$A$$.

   • $$116^\circ$$
   • $$29^\circ$$
   • $$26^\circ$$
   • $$90^\circ$$

5. If $$\tan 2A = \cot(A - 18^\circ)$$, where $$2A$$ is an acute angle, find the value of $$A$$.

   • $$36^\circ$$
   • $$108^\circ$$
   • $$18^\circ$$
   • $$90^\circ$$

6. If $$\tan A = \cot B$$, determine the value $$A + B = 90^\circ$$.

   • $$180^\circ$$
   • $$60^\circ$$
   • $$45^\circ$$
   • $$90^\circ$$

7. Simplify: $$\sec A(1 - \sin A)(\sec A + \tan A)$$

   • $$\frac{1 + \sin A}{\cos A}$$
   • $$\frac{1}{\cos A}$$
   • $$1 - \sin^2 A$$
   • $$1$$

8. If $$\sec\theta+\tan\theta=p$$, simplify the expression: $$\frac{p^2-1}{p^2+1}$$

   • $$\sec^2\theta + 1$$
   • $$2\sec^2\theta - 1$$
   • $$2\sec^2\theta - 1$$
   • $$\sin\theta$$