Warm Up:
Determine the following values:
sin160 =
sin20 =
sin200 =
sin340 =
Unit 5: Trigonometry
Day 6: The CAST Rule and Special Angles
Today we will....
1.
Learn the Special Angles and their corresponding trig ratios
2.
Combine our knowledge of the CAST Rule and Special Angles to find angles
and ratios without a calculator
Special Angles - 30 and 60
Construct an Equilateral triangle with side lengths 2. Drop a vertical line from the
top angle to the opposite side creating two Right-Triangles. The altitude will
bisect the opposite side since it is an equilateral triangle. Determine the length of
the altitude using the Pythagorean Theorem.
sin60 =
cos60 =
tan60 =
sin30 =
cos30 =
tan30 =
Special Angles: 45
Construct an Isosceles Right-Triangle and determine all 3 trig ratios of the non-90
angle. (Tip: The equal side lengths are 1 unit each)
sin45 =
cos45 =
tan45 =
Example 1: Find the exact values of the sine, cosine and tangent of 120ο.
1
Example 2: If cos 𝐴 = − √2 , determine the possible measures of angle A:
Example 3: If 0° ≤ 𝐴 ≤ 360°, find the possible measures of angle A when:
sin 𝐴 = −0.7845