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Home
- Algebra and trigonometry
- The unit circle: sine and cosine
- Unit circle
Key equations
Cosine |
|
Sine |
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Pythagorean Identity |
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Key concepts
- Finding the function values for the sine and cosine begins with drawing a unit circle, which is centered at the origin and has a radius of 1 unit.
- Using the unit circle, the sine of an angle
equals the
y -value of the endpoint on the unit circle of an arc of length
whereas the cosine of an angle
equals the
x -value of the endpoint. See
[link] .
- The sine and cosine values are most directly determined when the corresponding point on the unit circle falls on an axis. See
[link] .
- When the sine or cosine is known, we can use the Pythagorean Identity to find the other. The Pythagorean Identity is also useful for determining the sines and cosines of special angles. See
[link] .
- Calculators and graphing software are helpful for finding sines and cosines if the proper procedure for entering information is known. See
[link] .
- The domain of the sine and cosine functions is all real numbers.
- The range of both the sine and cosine functions is
- The sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle.
- The signs of the sine and cosine are determined from the
x - and
y -values in the quadrant of the original angle.
- An angle’s reference angle is the size angle,
formed by the terminal side of the angle
and the horizontal axis. See
[link] .
- Reference angles can be used to find the sine and cosine of the original angle. See
[link] .
- Reference angles can also be used to find the coordinates of a point on a circle. See
[link] .
Section exercises
Verbal
Discuss the difference between a coterminal angle and a reference angle.
Coterminal angles are angles that share the same terminal side. A reference angle is the size of the smallest acute angle,
formed by the terminal side of the angle
and the horizontal axis.
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Algebraic
For the following exercises, use the given sign of the sine and cosine functions to find the quadrant in which the terminal point determined by
lies.
For the following exercises, find the exact value of each trigonometric function.
Questions & Answers
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Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
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diveving the sum if all values
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The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits
Akshay
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Bright
a= 0.20233
b=0.3384
Sufiyan
How do I interpret level of significance?
It depends on your business problem or in Machine Learning you could use ROC- AUC cruve to decide the threshold value
Shivam
how skewness and kurtosis are used in statistics
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Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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