Graph of Cosine
Sine shifted left by π/2.
Key idea
Sine shifted left by π/2.
In depth
y = cos x is the same wave as sine shifted left by π/2. It starts at its maximum 1 when x = 0. It is an even function, symmetric about the y-axis.
Worked example
Key points: (0, 1), (π/2, 0), (π, −1), (3π/2, 0), (2π, 1).
Formula
Real-world uses
- Modelling the position of a pendulum bob at its start
- Alternating current voltage
Common mistake
Confusing the start point with sine.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Graph of Cosine?
Sine shifted left by π/2. It is a topic at the intermediate level in Trigonometry.
What is the formula for Graph of Cosine?
The key formula is y = cos x.
Where is Graph of Cosine used in real life?
Real-world examples: Modelling the position of a pendulum bob at its start; Alternating current voltage.
What should I learn before Graph of Cosine?
Make sure you are comfortable with Graph of Sine, the previous topic in Trigonometry.
What is a common mistake with Graph of Cosine?
Confusing the start point with sine.
How can I practise Graph of Cosine?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Graph of Cosine?
Move on to Graph of Tangent next.
Related intermediate topics in Trigonometry
- Radians – Angle measured by arc length on a unit circle; 2π rad = 360°.
- Converting Degrees and Radians – Multiply by π/180 or 180/π.
- Sine Ratio – Opposite over hypotenuse.
- Cosine Ratio – Adjacent over hypotenuse.
- Tangent Ratio – Opposite over adjacent.
- Reciprocal Trig Functions – Cosecant, secant and cotangent.