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**The Circular Functions (14.2)**

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A reference angle, ’, is the smallest, positive degree measure from the terminal side to the x-axis. (x, y) r ’ Use Pythagorean Theorem: x2 + y2 = r2 Note: x can be and y can be (depending on the Quadrant) Since r is the radius, it must be (+) because it is a length.

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**I. The Six Trigonometric Functions**

Cosine: cos = x Secant: sec = r r x Sine: sin = y Cosecant: csc = r r y Tangent: tan = y Cotangent: cot = x y x

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II. Sine and Cosine If the terminal ray of angle in standard position contains (x, y) on the unit circle, then cos = x and sin = y or (cos , sin ) = (x, y). b/c radius is always 1 -1 ≤ cos ≤ 1 and -1 ≤ sin ≤ 1 Look at x-values and y-values so far on the unit circle

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**A. Finding trig values using calculator:**

Example: Use a calculator. Round to the nearest four decimal places. a) Sin 45° .7071 b) cos 20° .9397 sin 45 enter cos 20 enter NOTE: Make sure your calculator is in degree mode.

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**B. Finding angles using trig values and a calculator:**

Example: If 0 < < 90, what is ? Round angles to the nearest tenth. a) sin b) cos 2nd sin .5299 enter You’re “undoing” sine = 32.0 2nd cos .7218 enter = 43.8 NOTE: Make sure your calculator is in degree mode.

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**I. The Six Trigonometric Functions**

Cosine: cos = x Secant: sec = r = r x cos Sine: sin = y Cosecant: csc = r = r y sin Tangent: tan = y = sin Cotangent: cot = x = cos x cos y sin

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**III. Using all Trig Functions**

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13.1 Right Triangle Trigonometry ©2002 by R. Villar All Rights Reserved.

13.1 Right Triangle Trigonometry ©2002 by R. Villar All Rights Reserved.

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