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Using the Sine and Cosine Addition Formulas to Prove Identities

":Applying the cosine addition and sine addition formulas proves the cofunction, add pi, and supplementary angle identities. Using the formulas, we see that sin(pi/2-x) = cos(x), cos(pi/2-x) = sin(x) ...

Using Sine to Calculate the Area of a Triangle

"Using the standard formula for the area of a triangle, we can derive a formula for using sine to calculate the area of a triangle. Using sine to calculate the area of a triangle means that we can fin ...

Unit Circle Coordinates

"The unit circle is a circle that has a radius of one and is centered at the origin of the coordinate plane. It is a concept that frequently occurs in many of the math subjects, especially those wher ...

Trigonometric Identities

"Identities are equations true for any value of the variable. Since a right triangle drawn in the unit circle has a hypotenuse of length 1, we define the trigonometric identies x=cos(theta) and y=sin( ...

Inverse Trigonometric Functions

"Once we understand the trigonometric functions sine, cosine, and tangent, we are ready to learn how to use inverse trigonometric functions to find the measure of the angle the function represents. In ...

Inverse Tangent Function

"Since tangent is not a one-to-one function, the domain must be limited to -pi/2 to pi/2, which is called the restricted tangent function. The graph of the inverse tangent function is a reflection of ...

Inverse Sine Function

"Since sine is not a one-to-one function, the domain must be limited to -pi/2 to pi/2, which is called the restricted sine function. The inverse sine function is written as sin^-1(x) or arcsin(x). I ...

Inverse Cosine Function

"Since cosine is not a one-to-one function, the domain must be limited to 0 to pi, which is called the restricted cosine function. The inverse cosine function is written as cos^-1(x) or arccos(x). I ...

Intercepts and Asymptotes of Tangent Functions

"The tangent identity is tan(theta)=sin(theta)/cos(theta), which means that whenever sin(theta)=0, tan(theta)=0, and whenever cos(theta)=0, tan(theta) is undefined (dividing by zero). When the tangen ...

The Law of Sines

"One method for solving for a missing length or angle of a triangle is by using the law of sines. The law of sines, unlike the law of cosines, uses proportions to solve for missing lengths. The ratio ...

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