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Cosine Is a Shifted Sine

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 6 of 49.

Most people think a plus inside the brackets moves a graph right. It moves it left. To draw the cosine, you moved the sine wave π/2 to the left. So $\cos\left(x\right) = \sin\left(x+\frac{\pi}{2}\right)$ .

The cosine reaches each height π/2 earlier than the sine. Earlier means further left on the graph. Adding inside the brackets moves a graph left. Subtracting moves it right.

$The sine and cosine waves on one axis: the cosine is the sine moved pi over 2 to the left$

Challenge

Draw $y = \sin\left(x+\frac{\pi}{4}\right)$ .

Then press Check.

Try it yourself

y = \sin\left(x+\frac{\pi}{4}\right)

Draw the wave

All lessons in Graphs of Trig Functions

2The Cosine Graph

The Cosine GraphCosine Is a Shifted SineWhere Sine Meets Cosine Cosine Graph Recap

5Midline

The Midline From Highest and Lowest Reading the Midline Midline Recap

8The Tangent Graph

The Tangent Graph Asymptotes Stretching the Tangent Graphs of sec, csc and cot Tangent Recap

3Amplitude

Amplitude: How Tall Amplitude of a Cosine A Negative a Flips It Amplitude From a Graph Amplitude Recap

6Phase Shift

Phase Shift: Sliding Phase Shift in Degrees Factor Out b First Reading a Phase Shift Phase Shift Recap

9Modelling with Waves

A Ferris Wheel Model Daylight Over a Year Tides Using a Model A Spring's Bounce Modelling Recap