From the following figure, which of the following is equal to $\tan (\theta/2)$?
From the following figure, which of the following is equal to $\tan (\theta/2)$?
May 2017
Solve for b as shown in the figure.
Solve for b as shown in the figure.
| A. $\sqrt{2} - 20$ | C. $12\sqrt{3} - 18$ |
| B. $6\sqrt{3} - 6$ | D. $4\sqrt{2} - 12$ |
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If $\theta$ is an acute angle of a right triangle where $\sin \theta = x/2$, compute the value of $\sin 2\theta$ in terms of $x$.
If $\theta$ is an acute angle of a right triangle where $\sin \theta = x/2$, compute the value of $\sin 2\theta$ in terms of $x$.
| A. $\dfrac{x}{\sqrt{4 - x^2}}$ | C. $2x \sqrt{4 - x^2}$ |
| B. $\frac{1}{2}x \sqrt{4 - x^2}$ | D. $\dfrac{\sqrt{4 - x^2}}{x}$ |
Find $\tan \beta$ from the given figure.
Find $\tan \beta$ from the given figure.
| A. 10/39 | C. 13/38 |
| B. 12/37 | D. 11/38 |
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From the given right triangle what is the value of $3 \sin^2 \varphi \, \sec \varphi$ in terms of $x$.
From the given right triangle what is the value of $3 \sin^2 \varphi \, \sec \varphi$ in terms of $x$.
| A. $\dfrac{x}{\sqrt{x^2 + 9}}$ | C. $\dfrac{x^2 + 9}{\sqrt{x^2 - 9}}$ |
| B. $\dfrac{9}{\sqrt{x^2 + 9}}$ | D. $\dfrac{x^2}{\sqrt{x^2 + 9}}$ |
Area outside equilateral triangle available for grazing by the goat.
The equilateral triangle ABC represents a wooden platform standing in a lawn. A goat is tied to a corner with a 15 ft. rope. What is the maximum amount of grazing area available to the goat.
Find the area of the sector inside the square ABCD.
Find the area of the sector inside the square ABCD. Dimensions shown are in centimeter.
| A. 52.36 cm2 | C. 48.32 cm2 |
| B. 64.36 cm2 | D. 32.94 cm2 |
Find the value of $x = \sin^2 \varphi - \cos^2 \varphi$ if $\varphi$ is $\pi / 4$ or $45^\circ$.
Find the value of $x = \sin^2 \varphi - \cos^2 \varphi$ if $\varphi$ is $\pi / 4$ or $45^\circ$.
| A. 3 | C. 1 |
| B. 2 | D. 0 |
Which of the following is equal to $\dfrac{\sin \theta}{1 + \cos \theta}$.
Which of the following is equal to $\dfrac{\sin \theta}{1 + \cos \theta}$.
| A. $\dfrac{\sin \theta}{2 \sin 2\theta}$ | C. $\dfrac{\sin \theta}{1 + \sin \theta}$ |
| B. $\dfrac{\cos \theta}{1 - \sin \theta}$ | D. $\dfrac{1 - \cos \theta}{\sin \theta}$ |
Find the value of x if $x = \dfrac{1 + \tan^2 \phi}{\tan \phi \, \csc^2 \phi}$.
Find the value of x if $x = \dfrac{1 + \tan^2 \varphi}{\tan \varphi \, \csc^2 \varphi}$.
| A. $\sin \varphi$ | C. $\tan \varphi$ |
| B. $\cos \varphi$ | D. $\csc \varphi$ |