Trigonometric Functions and Symmetries

The video explores the unit circle, focusing on angle theta in radians. It demonstrates flipping the terminal ray over the X and Y axes and calculates resulting angles. The video delves into trigonometric relationships, highlighting how sine and cosine values change with these transformations. It concludes by examining symmetries and reflections, encouraging viewers to explore these concepts further.

What is the angle called when it is flipped over the positive X-axis?

• Pi minus theta

• Negative theta

• Theta

• Pi plus theta

When an angle is flipped over the positive Y-axis, what is the resulting angle in terms of pi?

• Pi plus theta

• Pi minus theta

• Negative theta

• Theta

What is the angle when flipped over the negative X-axis?

• Theta

• Negative theta

• Pi plus theta

• Pi minus theta

What is the relationship between cosine of theta and cosine of negative theta?

• They are complementary

• They are supplementary

• They are negatives

• They are equal

How does the sine of negative theta relate to the sine of theta?

• They are complementary

• They are supplementary

• They are negatives

• They are equal

What is the sine of pi minus theta equal to?

• Sine of theta

• Negative cosine of theta

• Negative sine of theta

• Cosine of theta

What is the cosine of pi minus theta equal to?

• Sine of theta

• Negative cosine of theta

• Cosine of theta

• Negative sine of theta

What is the sine of theta plus pi equal to?

• Sine of theta

• Negative sine of theta

• Cosine of theta

• Negative cosine of theta

What is the cosine of theta plus pi equal to?

• Cosine of theta

• Negative sine of theta

• Sine of theta

• Negative cosine of theta

What concept is used to relate different angles and their trigonometric functions?

• Dilations

• Rotations

• Translations

• Symmetries