Warm-up 1) write 3 positive and 3 negative solutions to the equation:

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Presentation transcript:

Warm-up 1) write 3 positive and 3 negative solutions to the equation: 𝐜𝐨𝐬 𝒙 = 𝟑 𝟐 2) solve algebraically for 0≤𝑥≤360 𝟒 𝐬𝐢𝐧 𝒙 +𝟏𝟏=𝟏𝟒 3) solve with graphing calculator: give answers in radians 𝟓 𝐜𝐨𝐬 𝒙 =−.𝟖 4) find all solutions to the equation: 𝐬𝐢𝐧 𝜽 =−𝟏

Warm-up Identify the vertex of the parabola: 𝑦=2 (𝑥−5) 2 +6 Describe how each number of the equation above changes the graph, as compared to the graph of 𝑦= 𝑥 2

Trig Curves Transformed Graphing a Cosine Functions Draw one cycle of the function’s graph. Amplitude Period

Trig Functions Translation Graphing a Reflection Graph the function. Amplitude Period Reflection over x-axis

Trig Functions Translation Graphing a Reflection Graph the function. Amplitude Period Reflection over x-axis

Trig Functions Translation Translations of Trigonometric Graphs Translation of a Sine Function Amplitude Period

Rotating wheel problems Spokeless ferris wheel in china: 276ft diam. 22min/rev

Vernal and Autumn Equinox the time at which the sun crosses the plane of the equator towards the relevant hemisphere, making day and night of equal length. It occurs about March 21 in the N hemisphere (Sept 23 in the S hemisphere) A year is 365.242199 days.

Wave phenomena

The electro-magnetic spectrum

Radio telescope

Radio telescope array

Trig Curves Transformed Graph Sine, Cosine Functions

Trig Functions Translation Translations of Trigonometric Graphs Translation of a Sine Function Amplitude Period

Trig Functions Translation Graphing a Vertical Translation Graph the function. Amplitude Translation down 2 Period

Trig Functions Translation Graphing a Vertical Translation Graph the function. Amplitude Translation up 3 Period

Trig Functions Translation Graphing a Horizontal Translation Graph the function. Amplitude Period Translation right p

Trig Functions Translation Graphing a Horizontal Translation Graph the function. Amplitude Period Translation left p

Trig Functions Translation Graphing a Horizontal Translation Graph the function. Amplitude Period Translation right p/2

Transformations of sine and cosine Period, Amplitude, phase shift, and vertical shifts

𝟏𝟒𝟑° 𝟑𝟒° Inclination and Slope The inclination of a line is the angle 𝑎 , where 0 𝑜 ≤𝑎< 180 𝑜 , that is measured from the positive x-axis to the line. 𝟏𝟒𝟑° 𝟑𝟒°

Theorem For any line with slope 𝑚 and inclination 𝑎 𝑚= tan 𝑎 if 𝑎≠ 90 𝑜 . If 𝑎= 90 𝑜 , then the line has no slope. (The line is vertical.)

8.1 Simple Trigonometric Equations

Trig Curves Transformed Homework Sec 8.2 1- 15 odds