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Finding Exact Values of Trig Ratios. Special Right Triangles. 30-60-90. Special Right Triangles. 45-45-90. Consider the Special Angles in relation to the Unit Circle…. - PowerPoint PPT Presentation
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Finding Exact Values of Trig Ratios
Special Right Triangles
• 30-60-90
Special Right Triangles
• 45-45-90
Consider the Special Angles in relation to the Unit Circle…
• Since the radius is always 1 and we know that the sine, cosine, and tangent values are always determined by the point through which the terminal ray passes, we can construct the following….
30 Degree Angle
30sin 30cos 30tan
60 Degree Angle
60sin 60cos 60tan
45 Degree Angle
45sin 45cos 45tan
Values to Memorize
60 tan 45tan 30tan
60cos 45cos 30cos
sin60 45sin 30sin
Reference Angles
• We have previously learned that if the angle is the same size, then it will have the same values (but the + or – may switch depending upon the quadrant)
• A Reference Angle is the acute angle formed by the terminal ray and the x-axis– The Reference Angle tells us the size of the triangle
Examples
• Give the reference angle for each of the following angles:
315
Examples
• Give the reference angle for each of the following angles:
315 240
Examples
• Give the reference angle for each of the following angles:
315 240
6
5
Examples
• Give the reference angle for each of the following angles:
315 240
6
54
7
Reference Angles (in Radians)
• What can we observe about the reference angle in each radian measure?
Exact Values of Special Angles
• Find the exact value for each of the following:120sin
Exact Values of Special Angles
• Find the exact value for each of the following:120sin 150cos
Exact Values of Special Angles
• Find the exact value for each of the following:120sin 150cos 225tan
Exact Values of Special Angles
• Find the exact value for each of the following:120sin 150cos 225tan
6
7sin
Exact Values of Special Angles
• Find the exact value for each of the following:120sin 150cos 225tan
6
7sin
4
5cos
Exact Values of Special Angles
• Find the exact value for each of the following:120sin 150cos 225tan
6
7sin
4
5cos
3
4tan
Homework
• Pg. 280 (1-4, 11-18)