Unit 4 - Objective 3 - Values of Trigonometric Functions

Signs of trigonometric functions in all four Quadrants.

Reference Angles are always next to the x-axis

Given the reference angle , you can find the angle in the appropriate quadrant and given angle , you can find its reference angle.

The unit circle can be used to find trigonometric function for angles dividing the quadrants.

 On the unit circle x^2 + y^2 = 1 and x = cos y = sin

 Examples: sin 90° = y = 1 cos 90° = x = 0 tan 90° = y/x = 1/0 = undefined cot 90° = 1/tan 90° = x/y = 0/1 = 0 sec 90° = 1/cos 90° = 1/0 = undefined csc 90° = 1/sin 90° = 1/1 = 1

Special Triangles

Examples:

 1. Find the value for cos 150° 150° is in the 2nd quadrant, cos is negative in the 2nd quadrant, and the reference angle is180° - 150° = 30° So cos 150° = 2. Find for tan = if 0° < or = < 360° The reference angle for tan = is 30° and tan is positive in the 1st and 3rd quadrants so: is 30°, 180° + 30° = 210°

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