# What is the graph of y = sin^2 x + cos^2 x?

• MHB
• karush
In summary, "Act.trig.09" is a shortened term for "Actuarial trigonometry 09" which is a mathematical concept used in actuarial science to represent and analyze data using graphs and trigonometric functions. It differs from regular trigonometry in that it focuses on real-world applications and can be used in various fields such as finance, economics, and engineering. Some common graphs used in "Act.trig.09" include scatter plots, line graphs, and bar graphs. To learn more about "Act.trig.09" and graphing, one can utilize online resources, textbooks, and practice with real-world data sets.
karush
Gold Member
MHB

ok image to make sure I didn't have typo's
but I am clueless... I thot $y=\sin^2 x+cos^2 x$ was the graph of $y=1$

y=1 would be correct for the given function.

## 1. What does the graph of y = sin^2 x + cos^2 x look like?

The graph of y = sin^2 x + cos^2 x is a straight line at y = 1. This is because sin^2 x + cos^2 x always equals 1, regardless of the value of x.

## 2. Why does the graph of y = sin^2 x + cos^2 x always equal 1?

This is because of the Pythagorean identity, which states that sin^2 x + cos^2 x = 1 for all values of x. This is a fundamental property of trigonometric functions.

## 3. Is the graph of y = sin^2 x + cos^2 x periodic?

Yes, the graph of y = sin^2 x + cos^2 x is periodic with a period of 2π. This means that the graph repeats itself every 2π units along the x-axis.

## 4. How does changing the value of x affect the graph of y = sin^2 x + cos^2 x?

Changing the value of x will shift the graph of y = sin^2 x + cos^2 x horizontally, but it will not change the shape or height of the graph. This is because the value of sin^2 x + cos^2 x will always equal 1, regardless of the value of x.

## 5. What is the domain and range of the graph of y = sin^2 x + cos^2 x?

The domain of y = sin^2 x + cos^2 x is all real numbers, since x can take on any value. The range of the graph is [0,1], since the minimum value of sin^2 x + cos^2 x is 0 and the maximum value is 1.

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