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Cosine Is a Shifted Sine

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 8 of 51.

Lay the two graphs on one axis. The cosine reaches its top at 0°, the sine 90° later. Slide the sine graph 90° to the left and it lands exactly on the cosine graph: cos(x) = sin(x + 90°).

$The sine graph dashed and the cosine graph solid, the cosine 90 degrees to the left$

Why left? The sine reaches every height 90° after the cosine does, so the cosine at x is what the sine does at x + 90°. Adding to the angle inside the bracket moves a graph to the left, the opposite of what most people guess. Subtracting moves it to the right.

Challenge

Draw the graph on the goal row. Press Check.

Try it yourself

y=sin(x-pi/2)

Draw the graph

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Graphs of Trig Functions

2The Cosine Graph

Cosine: the Point's x 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