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Trigonometry : Trigonometry

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6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #13 : Finding Sides

Find the length of side .

Possible Answers:

5.11

3.28

4.08

4.67

Correct answer:

4.08

Explanation:

Recall the Law of Sines:

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Start by finding the value of angle :

A+47+49=180

A=84

Plug in the given values into the Law of Sines:

$\frac{3}{\sin 47}=\frac{a}{\sin 84}$

Rearrange the equation to solve for :

$a=(\sin 84)\frac{3}{\sin 47}=4.08$

Make sure to round to two places after the decimal.

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Example Question #14 : Finding Sides

If is between and degrees, and $\small \cos x = \frac{3}{5}$ , what is $\small \tan x$ ?

Possible Answers:

$\small \frac{5}{3}$

$\small \frac{4}{3}$

$\small \frac{3}{4}$

$\small \frac{3}{5}$

$\small \frac{4}{5}$

Correct answer:

$\small \frac{4}{3}$

Explanation:

Solution

Using Pythagoras theory, you can see that is . If is , than $\small \tan x$ is $\small \frac{4}{3}$ , because $\small \tan x$ is $\small \frac{opposite}{adjacent}$

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Example Question #1 : Unit Circle

What point corresponds to the angle $-\pi$ on the unit circle?

Possible Answers:

(1,1)

(1,0)

(-1,0)

(-1,-1)

(0,0)

Correct answer:

(-1,0)

Explanation:

The unit circle is the circle of radius one centered at the origin (0,0) in the Cartesian coordinate system. $-\pi$ is equivalent to $-180^{\circ}$ which corresponds to the point (-1,0) on the unit circle.

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Example Question #2 : Unit Circle

What point corresponds to an angle of $\frac{5\pi}{2}$ radians on the unit circle?

Possible Answers:

(-1,1)

(0,1)

(0,0)

(-1,-1)

(1,1)

Correct answer:

(0,1)

Explanation:

The unit circle is the circle of radius one centered at the origin (0,0) in the Cartesian coordinate system. $\frac{5\pi}{2}$ radians is equivalent to $\frac{5\pi}{2}\times \frac{180^{\circ}}{\pi}=450^{\circ}$ . This is a full circle $360^{\circ}$ plus a quarter-turn $90^{\circ}$ more. So, the angle $\frac{5\pi}{2}$ corresponds to the point (0,1) on the unit circle.

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Example Question #1 : Unit Circle

Give the angle between $0^{\circ}$ and $360^{\circ}$ that corresponds to the point (-1,0) .

Possible Answers:

$180^{\circ}$

$120^{\circ}$

$45^{\circ}$

$60^{\circ}$

$90^{\circ}$

Correct answer:

$180^{\circ}$

Explanation:

The angle $\pi$ or $180^{\circ}$ corresponds to the point (-1,0) .

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Example Question #3 : Unit Circle

What point corresponds to the angle $\frac{\pi}{2}$ on the unit circle?

Possible Answers:

(-1,-1)

(1,1)

(0,1)

(1,0)

(0,-1)

Correct answer:

(0,1)

Explanation:

The unit circle is the circle of radius one centered at the origin (0,0) in the Cartesian coordinate system. $\frac{\pi}{2}$ is equivalent to $90^{\circ}$ which corresponds to the point (0,1) on the unit circle.

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Example Question #2 : Unit Circle

Which of the following points is NOT on the unit circle?

Possible Answers:

(1,0)

(0, -1)

$(-\frac{1}{2}, -\frac{\sqrt{3}}{2})$

$(\frac{-\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$

$(\frac{\sqrt{3}}{2}, \frac{\sqrt{2}}{2})$

Correct answer:

$(\frac{\sqrt{3}}{2}, \frac{\sqrt{2}}{2})$

Explanation:

For a point to be on the unit circle, it has to have a radius of one. Therefore, the sum of the squares of point's coordinates must also equal one.

Let's try the point $(\frac{\sqrt{3}}{2}, \frac{\sqrt{2}}{2})$ .

$(\frac{\sqrt{3}}{2})^{2} + (\frac{\sqrt{2}}{2})^{2} = \frac{5}{4} \neq 1$

Therefore, this point is not on the unit circle.

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Example Question #1 : Unit Circle

When looking at the unit circle, what are the coordinates for an angle of $\frac{\pi}{4}$ ?

Possible Answers:

$\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)$

(0,1)

$\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$

$\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$

$(\sqrt{2},\sqrt{2})$

Correct answer:

$\left(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\right)$

Explanation:

The coordinates of the point on the circle for each angle are $(\cos\theta,\sin\theta)$ .

Since $\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}$ and $\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}$ , the point will be $(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2})$ .

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Example Question #1 : Unit Circle

What is the radius of the unit circle?

Possible Answers:

$\frac{3}{4}$

$\frac{1}{2}$

Correct answer:

Explanation:

By definition, the radius of the unit circle is 1.

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Example Question #1 : Unit Circle

What point corresponds to the angle $\frac{\pi}{3}$ on the unit circle?

Possible Answers:

$\left(\frac{1}{2},\frac{1}{2}\right)$

(0,-1)

$\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$

$\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)$

(1,1)

Correct answer:

$\left(\frac{1}{2},\frac{\sqrt{3}}{2}\right)$

Explanation:

In order to find the point corresponds to the angle $\frac{\pi}{3}$ on the unit circle we can write:

$t=\frac{\pi}{3}\ or\ 60^{\circ}$

In the unit circle which has the radious of R=1 we can write:

$cos\ t=\frac{x}{R}=\frac{x}{1}=x\Rightarrow x=cos(60^{\circ})=\frac{1}{2}$

$sin\ t=\frac{y}{R}=\frac{y}{1}=y\Rightarrow y=sin(60^{\circ})=\frac{\sqrt{3}}{2}$

So the point corresponds to the angle $\frac{\pi}{3}$ on the unit circle is $(\frac{1}{2},\frac{\sqrt{3}}{2})$

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Trigonometry : Trigonometry

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #13 : Finding Sides

Example Question #14 : Finding Sides

Example Question #1 : Unit Circle

Example Question #2 : Unit Circle

Example Question #1 : Unit Circle

Example Question #3 : Unit Circle

Example Question #2 : Unit Circle

Example Question #1 : Unit Circle

Example Question #1 : Unit Circle

Example Question #1 : Unit Circle

All Trigonometry Resources

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