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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 ...

The Law of Cosines

"One method for solving for a missing length or angle of a triangle is by using the law of cosines. The law of cosines, unlike the law of sines, is similar to the Pythagorean theorem, but it works for ...

Tangent Transformation

"When graphing a tangent transformation, start by using a theta and tan(theta) t-table for -pi/2 to pi/2. In the case of y=Atan(Bx) or y=Atan(B(x-h)), define Bx or B(x-h) to be equal to theta and sol ...

Tangent Ratios

"Right triangles have ratios that are used to represent their base angles. Tangent ratios, along with cosine and sine ratios, are ratios of two different sides of a right triangle. Tangent ratios are ...

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