Topics
>
Precalculus>
Unit Circle>
Unit Circle: Find Angles from Equations>
Unit Circle: Find Angles from EquationsUnit Circle: Find Angles from Equations
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 3 questions completed
Questions:
- 1
- 2
- 3
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- Answered
- Review
-
Question 1 of 3
1. Question
Given that `0≥theta≥360`, solve:`cos theta=- 1/sqrt2`- `theta=` (135, 225)`°,` (225, 135)`°`
Hint
Help VideoCorrect
Well Done!
Incorrect
Trigonometric Functions
$$\sin\theta=\frac{\color{#9a00c7}{\text{opposite}}}{\color{#007DDC}{\text{hypotenuse}}}$$$$\cos\theta=\frac{\color{#00880A}{\text{adjacent}}}{\color{#007DDC}{\text{hypotenuse}}}$$$$\tan\theta=\frac{\color{#9a00c7}{\text{opposite}}}{\color{#00880A}{\text{adjacent}}}$$
Positive Values in the Unit Circle
Quadrant I: AllQuadrant II: Sine onlyQuadrant III: Tangent onlyQuadrant IV: Cosine onlyExact Triangle Ratios
The acute angle `(theta’)` is an angle less than `90°` and is relative to the horizontal axis.First, identify which quadrant `theta` may lie.Since the given cosine value is negative, `theta` may be on Quadrant II or III.
Next, get the acute angle (`theta’`) for `theta`.We can do this by matching the value of `cos theta` to an Exact Triangle.$$\cos\theta=\frac{\color{#00880A}{\text{adjacent}}}{\color{#007DDC}{\text{hypotenuse}}}=-\frac{\color{#00880A}{1}}{\color{#007DDC}{\sqrt2}}$$
Since `1` is the adjacent side and `sqrt2` is the hypotenuse, `theta’=45°`Now, find the corresponding angle of the acute angle in both Quadrant II and III.Quadrant II:`180°-45°=``135°`
Quadrant III:`180°+45°=``225°`
Therefore, `theta=135°,225°``theta=135°,225°` -
Question 2 of 3
2. Question
Given that `0≥theta≥360`, solve:`sin theta=(sqrt3)/2`- `theta=` (60, 120)`°,` (120, 60)`°`
Hint
Help VideoCorrect
Fantastic!
Incorrect
Trigonometric Functions
$$\sin\theta=\frac{\color{#9a00c7}{\text{opposite}}}{\color{#007DDC}{\text{hypotenuse}}}$$$$\cos\theta=\frac{\color{#00880A}{\text{adjacent}}}{\color{#007DDC}{\text{hypotenuse}}}$$$$\tan\theta=\frac{\color{#9a00c7}{\text{opposite}}}{\color{#00880A}{\text{adjacent}}}$$
Positive Values in the Unit Circle
Quadrant I: AllQuadrant II: Sine onlyQuadrant III: Tangent onlyQuadrant IV: Cosine onlyExact Triangle Ratios
The acute angle `(theta’)` is an angle less than `90°` and is relative to the horizontal axis.First, identify which quadrant `theta` may lie.Since the given sine value is positive, `theta` may be on Quadrant I or II.
Next, get the acute angle (`theta’`) for `theta`.We can do this by matching the value of `sin theta` to an Exact Triangle.$$\sin\theta=\frac{\color{#9a00c7}{\text{opposite}}}{\color{#007DDC}{\text{hypotenuse}}}=\frac{\color{#9a00c7}{\sqrt3}}{\color{#007DDC}{2}}$$
Since `sqrt3` is the opposite side and `2` is the hypotenuse, `theta’=60°`Now, find the corresponding angle of the acute angle in both Quadrant I and II.Quadrant I:`60°`
Quadrant II:`180°-60°=``120°`
Therefore, `theta=60°,120°``theta=60°,120°` -
Question 3 of 3
3. Question
Given that `0≥x≥360`, solve:`tan x=-1`- `x=` (135, 315)`°,` (135, 315)`°`
Hint
Help VideoCorrect
Great Work!
Incorrect
Trigonometric Functions
$$\sin\theta=\frac{\color{#9a00c7}{\text{opposite}}}{\color{#007DDC}{\text{hypotenuse}}}$$$$\cos\theta=\frac{\color{#00880A}{\text{adjacent}}}{\color{#007DDC}{\text{hypotenuse}}}$$$$\tan\theta=\frac{\color{#9a00c7}{\text{opposite}}}{\color{#00880A}{\text{adjacent}}}$$Positive Values in the Unit Circle
Quadrant I: AllQuadrant II: Sine onlyQuadrant III: Tangent onlyQuadrant IV: Cosine onlyExact Triangle Ratios
The acute angle `(theta’)` is an angle less than `90°` and is relative to the horizontal axis.First, identify which quadrant `x` may lie.Since the given tangent value is negative, `x` may be on Quadrant II or IV.
Next, get the acute angle for `x`.We can do this by matching the value of `tan x` to an Exact Triangle.$$\tan x=\frac{\color{#9a00c7}{\text{opposite}}}{\color{#00880A}{\text{adjacent}}}=-\frac{\color{#9a00c7}{1}}{\color{#00880A}{1}}$$
Since `1` is the opposite side and `1` is the adjacent, the acute angle is `45°`Now, find the corresponding angle of the acute angle in both Quadrant II and IV.Quadrant II:`180°-45°=``135°`
Quadrant IV:`360°-45°=``315°`
Therefore, `x=135°,315°``x=135°,315°`