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Sine Definition

"The right triangle definitions of sine and cosine only apply to acute angles, so a more complete definition is needed. The point where the terminal side intersects the unit circle (x, y) is the basi ...

Sine and Cosine Transformations

"The coefficients A and B in y=Asin(Bx) or y=Acos(Bx) each have a different effect on the graph. If A and B are 1, both graphs have an amplitude of 1 and a period of 2pi. For sine and cosine transfor ...

Evaluating Sine

"If you want to make your math life incredibly easier, memorize the sine and cosine values for pi/3, pi/4, and pi/6, as well as 0, pi/2, and pi. These values constantly reappear throughout Trigonomet ...

Sine and Cosine Graphs

"Sine and cosine are periodic functions, which means that sine and cosine graphs repeat themselves in patterns. You can graph sine and cosine functions by understanding their period and amplitude. ...

Sine Addition Formula

"Starting with the cofunction identities, the sine addition formula is derived by applying the cosine difference formula. There are two main differences from the cosine formula: (1) the sine addition ...

Evaluating Cosine

"To find the value of sine and cosine at non-acute angles (from 90 to 360), first draw the angle on the unit circle and find the reference angle. A reference angle is formed by the terminal side and ...

Euler Formula

"One formula that is used frequently to rewrite a complex number is the Euler Formula. The Euler Formula can be used to convert a complex number from exponential form to rectangular form and back. The ...

Equation of a Circle

"A circle can't be represented by a function, as proved by the vertical line test. However, we can obtain an equation that describes the full circle by using the distance formula between the given cen ...

Secant and Cosecant

"To graph secant and cosecant, find values of the reciprocal functions and plot them on the coordinate plane. Unlike the graphs of sine and cosine, secant and cosecant have vertical asymptotes wheneve ...

Double Angle Formulas

"The double angles sin(2theta) and cos(2theta) can be rewritten as sin(theta+theta) and cos(theta+theta). Applying the cosine and sine addition formulas, we find that sin(2theta)=2sin(theta)cos(theta ...

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