Trigonometry on the Coordinate Plane -...
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Trigonometry on the Coordinate Plane
Essential Question: How do you find the exact value of a trig function on
the coordinate plane?
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What is trigonometry?• Trigonometry is the
branch of mathematics that studies the relationships between the sides of triangles and their angles.
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The Six Basic Trig Functions• Main Trig Functions
– Sine– Cosine– Tangent
• Reciprocal Functions– Cosecant– Secant– Cotangent
When given an angle, these trig functions tell you the ratio of the sides of the triangle.
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sin
cos
tan
ohahoa
θ
θ
θ
=
=
=
csc
sec
cot
hohaao
θ
θ
θ
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=
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Reference Triangles
• You can use reference triangles to find the exact value of the trig functions.
• Reference triangles are quick easy relationships between the sides of the triangle with the special angles of 30˚, 60˚ and 45˚.
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60°
30°
12
360°
30°
1
23
45°
45°
1
1
2
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Degrees and Radians
• The angles of the trig functions can be measured using degrees or radians.
• In AP Calculus typically the angles are measured in radians.
• You need to be able to convert between both.
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Degrees Radians
30° π/6
45° π/4
60° π/3
90° π/2
180° π
360° 2π
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Finding Trig Functions on the Coordinate Plane
• Convert the angle to degrees if necessary.• Draw the angle in the correct quadrant on the coordinate
plane.• Form a triangle (using the angle) perpendicular to the x-axis.• Find the angle between the hypotenuse and the x-axis inside
the drawn triangle.• Label the triangle using a reference triangle.• Choose the correct sides of the triangle for the needed ratio.• Check the sign of the function in the quadrant.• Reduce if possible. Don’t give decimal answers!
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90°
0 / 360° °180°
270°
AllSin
Tan Cos
+
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sin135°
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cot 315°−
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csc 45°
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cos 45°−
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sec60°
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tan135°
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cot120°
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sin 45°
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tan 210°
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cot 30°
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• How do you find the exact value of a trig function on the coordinate plane?