Unit 3 Intro to Trig (Chap 4.1-4.4 in Book)

Unit Circle

A circle centered at the point (0,0) with a radius of 1. Sine and Cosine correspond to y and x respectively.

Initial Side and Terminal Side of an angle

An angle is formed by a rotating a ray about it's endpoint. The Starting position is the initial side. The ending position is the terminal side.

Supplementary Angles

Angles that add to 180⁰ or π radians

Complementary Angles

Angles that add to 90⁰ or π/2 radians

Coterminal Angles

Angles with the same terminal side. Find Positive coterminal angles by adding 360° (or 2π). find Negative coterminal angles by subtracting 360° (or 2π).

Sector Area of a Circle

Area = (θr²/2) where θ is measured in radians. If given degrees convert to Radians first.

Arc Length

For a circle of radius r, a central angle of θ intercepts an arc length given by... s=rθ. where θ is measured in radians. Remember if given degrees you must convert to radians first.

Convert from Radians to Degrees

Multiply by 180⁰/π. Remember value you are going to is on top of ratio Ex. π/9 radians = (π/9) × (180⁰/π) = 20⁰

Convert from Degrees to Radians

Multiply by π/180⁰. Remember value you are going to is on top of ratio. Ex. 36⁰ × (π/180⁰) = π/5 radians.

Radian

One radian is the measure of the central angle that intercepts an arc of equal length to the radius of the circle. 1rad ≈ 57.3°.

In what quadrants are Sine, Cosine, and Tangent positive or negative?

Remember All Students Take Classes represents the positive values of each Quadrant.

The Six Trigometric Functions

Sine, Cosine, Tangent, Cosecent, Secant, Cotangent.

Standard Position

Standard position where the initial side of an angle is located on the positive X axis.

Trigonometry

The Study of Triangles

Reference Angle

The acute angle θ' formed by the terminal side of θ and the horizontal axis or x axis.

If the angle given in a unit circle is positive it rotates _____ and if it is negative it rotates _____

counterclockwise, clockwise

Finding the radius from x and y.

r = √(x²+y²)

Reciprocal Identities

sin θ = (1/csc θ) ; csc θ = (1/sin θ) cos θ = (1/sec θ); sec θ = (1/cos θ) tan θ = (1/cot θ); cot θ = (1/tan θ)

Trigometric Functions at Any Angle

sin θ = y/r so csc θ = r/y , y≠0 cos θ = x/r so sec θ = r/x , x≠ 0 tan θ = y/x , x≠0 so cot θ = x/y , y≠0

Right Triangle Definitions of Trig Functions. SOH CAH TOA

sin θ=(opp/hyp) , csc θ=(hyp/opp) cos θ = (adj/hyp), sec θ = (hyp/adj) tan θ = (opp/adj), cot θ= (adj/opp)

Quotient Identities

tan θ = (sin θ/cos θ) cot θ = (cosθ/sin θ)