Solving Equations with Trig Functions

Labeling a right triangle A

Practice Name the side (Opposite or Adjacent) to the given angle. A B C Hypotenuse: Opposite of <C: Adjacent to <C: Opposite of <A: Adjacent to <A:

Practice Name the side (Opposite or Adjacent) to the given angle. L S U Hypotenuse: Opposite of <S: Adjacent to <S: Opposite of <U: Adjacent to <U:

Practice Name the side (Opposite or Adjacent) to the given angle. A B T Hypotenuse: Opposite of <A: Adjacent to <A: Opposite of <B: Adjacent to <B:

Practice Name the side (Opposite or Adjacent) to the given angle. X A E Hypotenuse: Opposite of <X: Adjacent to <X: Opposite of <E: Adjacent to <E:

Trig Functions Trig Ratios of angles of a right triangle relates the sides of the right triangle Sine: sin A = Opposite/Hypotenuse Cosine: cos A =Adjacent/Hypotenuse Tangent: tan A = Opposite/Adjacent

Example (Soh-Cah-Toa) Find all three trig ratios of the following triangle: sin A = cos A = tan A =

Using Pythagorean Theorem If only 2 sides of the triangle are given, use the Pythagorean Theorem to solve for the missing side a 2 + b 2 = c 2

Example A B C sin A = cos A = tan A =

Example A = 12 cm, C = 15 cm sin A = cos A = tan A =

Simplifying Radicals

Perfect Squares

= 2 = = 5 = = This is a piece of cake! Simplify

= = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

= = = = = Simplify = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

Combining Radicals + To combine radicals: combine the coefficients of like radicals

Simplify each expression

Simplify each expression: Simplify each radical first and then combine.

= = = = = Simplify = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM

You Try

Simplify each expression

Multiplying Radicals * To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.

Multiply and then simplify

Dividing Radicals To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator

That was easy!

This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. 42 cannot be simplified, so we are finished.

This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.

This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. Reduce the fraction.

= X = = = = Simplify

= = = =

= = = = ?