finding exact values of trig ratios. special right triangles 30-60-90
TRANSCRIPT
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Finding Exact Values of Trig Ratios
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Special Right Triangles
• 30-60-90
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Special Right Triangles
• 45-45-90
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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….
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30 Degree Angle
30sin 30cos 30tan
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60 Degree Angle
60sin 60cos 60tan
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45 Degree Angle
45sin 45cos 45tan
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Values to Memorize
60 tan 45tan 30tan
60cos 45cos 30cos
sin60 45sin 30sin
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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
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Examples
• Give the reference angle for each of the following angles:
315
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Examples
• Give the reference angle for each of the following angles:
315 240
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Examples
• Give the reference angle for each of the following angles:
315 240
6
5
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Examples
• Give the reference angle for each of the following angles:
315 240
6
54
7
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Reference Angles (in Radians)
• What can we observe about the reference angle in each radian measure?
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Exact Values of Special Angles
• Find the exact value for each of the following:120sin
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Exact Values of Special Angles
• Find the exact value for each of the following:120sin 150cos
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Exact Values of Special Angles
• Find the exact value for each of the following:120sin 150cos 225tan
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Exact Values of Special Angles
• Find the exact value for each of the following:120sin 150cos 225tan
6
7sin
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Exact Values of Special Angles
• Find the exact value for each of the following:120sin 150cos 225tan
6
7sin
4
5cos
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Exact Values of Special Angles
• Find the exact value for each of the following:120sin 150cos 225tan
6
7sin
4
5cos
3
4tan
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Homework
• Pg. 280 (1-4, 11-18)