3. Text Example Let P = (-3, -4) be a point on the terminal side of . Find each of the six trigonometric functions of . Solution The situation is shown below. We need values for x , y , and r to evaluate all six trigonometric functions. We are given the values of x and y . Because P = (-3, -4) is a point on the terminal side of , x = -3 and y = -4. Furthermore, r x = -3 y = -4 P = (-3, -4) x y -5 5 -5 5
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5. The Signs of the Trigonometric Functions x y Quadrant II Sine and cosecant positive (-,+) Quadrant I All functions positive (+,+) Quadrant III tangent and cotangent positive (-,-) Quadrant IV cosine and secant positive (+,-)
6. Example: Evaluating Trigonometric Functions Given tan = -2 / 3 and cos > 0, find cos and csc . Solution Because the tangent is negative and the cosine is positive, lies in quadrant IV. This will help us to determine whether the negative sign in tan = -2 / 3 should be associated with the numerator or the denominator. Keep in mind that in quadrant IV, x is positive and y is negative. Thus, In quadrant IV, y is negative. x = 3 y = -2 P = (3, -2) x y -5 5 -5 5 r = 13 Thus, x = 3 and y = -2. Furthermore, Now that we know x , y and r , find cos and csc .
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11. Example: Using Reference Angles to Evaluate Trigonometric Functions Use reference angles to find the exact value of each of the following trigonometric functions. a. sin 135° x y 135° 45° more more x y 4 / 3 / 3 x y / 3 - / 3
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