Trigonometry Lecture Notes Section 2.1Page 1 of 5
Section 2.1: Trigonometric Functions of Acute Angles
Big Idea:If we restrict an angle in standard position to be an acute angle, then a right triangle is formed by dropping a vertical from the point on the terminal side to the x axis
Big Skill:You should be able to .
Right Triangle Based Definitions of Trigonometric Functions (Section 2.1)(SOH CAH TOA)
Cofunction Identities (Section 2.1)
For any acute angle A,
Practice:
- Practice the right triangle definitions of an acute angle using a 36 – 77 – 85 right triangle, and a right triangle with sides of length 1 and 2.
- Show why the cofunction identities are true.
- Solve for :
- State how the sine, cosine, and tangent functions increase or decrease with increasing angle.
Trigonometric Function Values of Special Angles
The trigonometric Values of a 45 angle can be derived by thinking of an isosceles right triangle. Compute the length of the hypotenuse for the triangle below, and then use the side lengths to derive all trigonometric function values for an angle of 45
Trigonometric Function Values for 45 (Section 2.1)The trigonometric values of 30 and 60 angles can be derived by thinking of the triangles formed when an equilateral triangle is bisected. Compute the length of the altitude formed by bisecting the equilateral triangle below, and then use the side lengths to derive all trigonometric function values for angles of 30 and 60.
Trigonometric Function Values for 30 and 60 (Section 2.1)The trigonometric values of 36 and 72 angles can be derived by starting with a 36-72-72 isosceles triangle, bisecting one of the base angles, deriving relationships between the side lengths using similar triangles, and then bisecting the apex angle to form right triangles. Perform these calculations using the 36-72-72 isosceles triangle below, and then use the side lengths to derive all trigonometric function values for angles of 36 and 72.
Trigonometric Function Values for 36 and 72 (Section 2.1 Mirus Special)