Trigonometry in the Coordinate Plane: Sine, Cosine, and Tangent

This lesson covers the basics of trigonometry, focusing on sine, cosine, and tangent in the coordinate plane. It begins with a review of right triangle geometry and the Pythagorean theorem, introducing the acronym SOHCAHTOA for remembering trigonometric ratios. The lesson explains angles in standard position and how to use reference triangles to find trigonometric ratios. It also discusses the rotation of terminal rays and how to calculate sine and cosine at 90 degrees. An example problem is provided to illustrate these concepts, along with tips to avoid common mistakes.

What is the acronym used to remember the basic trigonometric functions?

• COSINE

• SOHCAHTOA

• TRIGON

• Pythagorean

Why can't SOHCAHTOA be used to find the sine, cosine, or tangent of a 90-degree angle?

• Because the adjacent side is zero

• Because the angle is not acute

• Because the opposite side is zero

• Because the hypotenuse is undefined

In the coordinate plane, what does the hypotenuse of the reference triangle represent?

• The x-coordinate

• The y-coordinate

• The radius of a circle

• The slope of the line

What is the sine of a 90-degree angle using the coordinate method?

• r

• 0

• Undefined

• 1

If a point on the terminal ray is (3, 4), what is the hypotenuse of the reference triangle?

• 3

• 7

• 4

• 5

What is the sine of the angle if the terminal ray passes through the point (3, 4)?

• 3/5

• 4/5

• 5/4

• 5/3

How can you remember which axis corresponds to x and y?

• x is vertical, y is horizontal

• x is horizontal, y is vertical

• Both are vertical

• Both are horizontal