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Using Trigonometric Identities

"When simplifying problems that have reciprocal trig functions, start by substituting in the identities for each. If possible, write tangent in terms of sine and cosine. Use algebra to eliminate any ...

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 ...

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( ...

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 ...

Square Root Operations

"Since Pythagorean theorem proofs requires us to square numbers and find square roots, reviewing square root operations from Algebra is really important. When working with the Pythagorean theorem, it ...

Solving Trigonometric Equations

"When solving trigonometric equations, we find all the angles that make the equation true. If there is no interval given, use periodicity to show the infinite number of solutions. Two ways to visuali ...

Evaluating the Tangent Function

"When evaluating the tangent function, to find values of the tangent function at different angles, we first identify the reference angle formed by the terminal side and the x-axis. Then, we find the t ...

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