Unit Circle: Exact Values 1
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 4 questions completed
Questions:
- 1
- 2
- 3
- 4
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
- 4
- Answered
- Review
-
Question 1 of 4
1. Question
Find the exact value of:`sin330°`Hint
Help VideoCorrect
Excellent!
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 onlyFirst, draw in the ray of `330°`.
Next, get the acute angle (`theta’`) for `330°`.The acute angle is an angle less than `90°` and is relative to the horizontal axis.
Based on this diagram, simply subtract `330°` from `360°` to get the acute angle.`theta’` `=` `360°-330°` `=` `30°` Now, identify if sine is positive or negative in the quadrant where the ray lies, Quadrant IV.
The sine value is negative in Quadrant IV.Finally, we can get the exact value of `sin330°` by solving for `-sin30°` using Exact Triangle Ratios.
`sin330°` `=` `-sin30°` `=` $$-\frac{\color{#9a00c7}{\text{opposite}}}{\color{#007DDC}{\text{hypotenuse}}}$$ `=` $$-\frac{\color{#9a00c7}{1}}{\color{#007DDC}{2}}$$ `-1/2` -
Question 2 of 4
2. Question
Find the exact value of:`tan120°`Hint
Help VideoCorrect
Nice Job!
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 onlyFirst, draw in the ray of `120°`.
Next, get the acute angle (`theta’`) for `120°`.The acute angle is an angle less than `90°` and is relative to the horizontal axis.
Based on this diagram, simply subtract `120°` from `180°` to get the acute angle.`theta’` `=` `180°-120°` `=` `60°` Now, identify if tangent is positive or negative in the quadrant where the ray lies, Quadrant II.
The tangent value is negative in Quadrant II.Finally, we can get the exact value of `tan120°` by solving for `-tan60°` using Exact Triangle Ratios.
`tan120°` `=` `-tan60°` `=` $$-\frac{\color{#9a00c7}{\text{opposite}}}{\color{#00880A}{\text{adjacent}}}$$ `=` $$-\frac{\color{#9a00c7}{\sqrt3}}{\color{#00880A}{1}}$$ `=` `-sqrt3` `-sqrt3` -
Question 3 of 4
3. Question
Find the exact value of:`sec315°`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 onlyFirst, draw in the ray of `315°`.
Next, get the acute angle (`theta’`) for `315°`.The acute angle is an angle less than `90°` and is relative to the horizontal axis.
Based on this diagram, simply subtract `315°` from `360°` to get the acute angle.`theta’` `=` `360°-315°` `=` `45°` Finally, we can get the exact value of `sec315°` by solving for `sec45°` using Exact Triangle Ratios.Note that since `sec theta=1/(cos theta)` and cosine is positive in Quadrant IV, secant is also positive.
`sec315°` `=` `sec45°` `=` `1/(cos45°)` `=` $$\frac{1}{\frac{\color{#9a00c7}{\text{opposite}}}{\color{#00880A}{\text{adjacent}}}}$$ `=` $$\frac{1}{\frac{\color{#9a00c7}{1}}{\color{#00880A}{\sqrt2}}}$$ `=` `sqrt2` `sqrt2` -
Question 4 of 4
4. Question
Find the exact value of:`cot150°`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 onlyFirst, draw in the ray of `150°`.
Next, get the acute angle (`theta’`) for `150°`.The acute angle is an angle less than `90°` and is relative to the horizontal axis.
Based on this diagram, simply subtract `150°` from `180°` to get the acute angle.`theta’` `=` `180°-150°` `=` `30°` Now, identify if cotangent is positive or negative in the quadrant where the ray lies, Quadrant II.
The cotangent value is negative in Quadrant II.Finally, we can get the exact value of `cot150°` by solving for `-cot30°` using Exact Triangle Ratios.Note that `cot theta = 1/(tan theta)`
`cot150°` `=` `-cot30°` `=` `- 1/(tan30°)` `=` $$-\frac{1}{\frac{\color{#9a00c7}{\text{opposite}}}{\color{#00880A}{\text{adjacent}}}}$$ `=` $$-\frac{1}{\frac{\color{#9a00c7}{1}}{\color{#00880A}{\sqrt3}}}$$ `=` `-sqrt3` `-sqrt3`