Trigonometry on the Coordinate Plane

Essential Question: How do you find the exact value of a trig function on

the coordinate plane?

What is trigonometry?• Trigonometry is the

branch of mathematics that studies the relationships between the sides of triangles and their angles.

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.

sin

cos

tan

ohahoa

θ

θ

θ

=

=

=

csc

sec

cot

hohaao

θ

θ

θ

=

=

=

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˚.

60°

30°

12

360°

30°

1

23

45°

45°

1

1

2

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.

Degrees Radians

30° π/6

45° π/4

60° π/3

90° π/2

180° π

360° 2π

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!

90°

0 / 360° °180°

270°

AllSin

Tan Cos

+

sin135°

cot 315°−

csc 45°

cos 45°−

sec60°

tan135°

cot120°

sin 45°

tan 210°

cot 30°

• How do you find the exact value of a trig function on the coordinate plane?