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Area of a Sector of a Circle \(= \ (\frac{θ}{360}) \times πr^2\)
Arc length \(= \ \frac{Central \ Angle}{360°} \times 2πr\)
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In a right triangle, when one side and an angle are given we can find a missing side. The trigonometric ratios can be used to determine the length of the missing side in a right triangle.
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- Step 1: Draw the terminal side of the angle.
- Step 2: Find reference angle. (It is the smallest angle that you can make from the terminal side of an angle with the \(x\)-axis.)
- Step 3: Find the trigonometric function of the reference angle.
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Degrees \(=\) Radians \(\times \frac{180}{π}\)
Example:
Convert \(\frac{ 2π}{3}\) to degrees.
\(\frac{2\ π}{3} \times \frac{180}{π} \ = \ \frac{360π}{3π} \ = \ 120\)
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radians \(=\) degrees \(\times \frac{π}{180}\)
Example:
Convert \(150\) degrees to radians.
radians \(= \ 150 \times \frac{π}{180} \ = \ \frac{5π}{6}\)
 
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- Co-terminal angles are equal angles.
- To find a co-terminal of an angle, add or subtract \(360\) degrees (or \(2π\) for radians) to the given angle.
- Reference angle is the smallest angle that you can make from the terminal side of an angle with the \(x-\)axis.
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A standard-position angle has its vertex at the plane's origin. Along the positive \(x\)-axis is where its initial ray (beginning side) is located. From the beginning side, its terminal ray (finishing side) travels counterclockwise.
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Sine, Cosine, Tangent, Cotangent, Secant, and Cosecant are trigonometric ratios. For these trigonometric ratios, the standard angles are \(0, \ 30, \ 45, \ 60,\) and \(90\) degrees. These angles can also be shown using radians, such as \(0, \ \frac{π}{6}, \ \frac{π}{4}, \ \frac{π}{3},\) and \(\frac{π}{2}\) . In trigonometry, these angles are most regularly and frequently used. To solve many problems, you need to know the values of these trigonometry angles.
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A geometric series with an infinite number of terms is called an infinite geometric series. The infinite geometric series is shown as \(a, \ ar, \ ar^2, \ ar^3, \ ... \ ,\) to \(∞\).
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Finite Geometric Series:  The sum of a geometric series is finite when the absolute value of the ratio is less than 1.
\(s_n=\sum_{i=1}^n ar^{i-1} =a_1 \frac{(1-r^n)}{(1-r)}\)
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