14.2 The Circular Functions

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Presentation transcript:

14.2 The Circular Functions Locate the points on the unit circle and identify the angle measure in standard position that would pass through that point.

Circular Functions Defined: Circular Functions Defined: ** All angles in standard position – on the UNIT CIRCLE 1. The sine function or sin sin 90° 180° 270° 360°

Circular Functions Defined: Circular Functions Defined: ** All angles in standard position - on the UNIT CIRCLE. 2. The cosine function or cos cos 0° 90° 180° 270° 38°

Four more circular functions defined: (Where (x,y) is the point of intersection of the terminal ray and the unit circle!!)

1) An angle has a tangent of 1. 5 and it is in the 3rd quadrant 1) An angle has a tangent of 1.5 and it is in the 3rd quadrant. What is the sine of this angle?

2) A terminal ray contains the point (4,-3) 2) A terminal ray contains the point (4,-3). Find the exact values of the six trig functions for the angle associated with this point. Then, find the measure of the positive angle to the nearest degree.

3) Use your calculator to find the following to the thousandths place. a) sin 42° b) cos 42° c) tan 42° d) cot 42° e) sec 42° f) csc 42°

The Pythagorean Identities

Back to Problem #1: An angle has a tangent of 1 Back to Problem #1: An angle has a tangent of 1.5 and it is in the 3rd quadrant. What is the sine of this angle? How can we use the trig identity?