Trigonometry Handout

More documents

Recommendations

Info

<strong>Trigonometry</strong> π Note: You could have also formed the right triangle with θ = and made the appropriate 4 sign changes for the quadrant you were in. Example 4: Let sin − 5 3π θ = where π < θ < . Find the values of the other trigonometric 6 2 functions. Solution: 5 6 x = 11 θ We know that θ is in the 3 rd Quadrant. Thus, only tangent and cotangent have positive signs. Every thing else will be negative. For now we will just drop the signs to form a right triangle with hyp = 6 and opp = 5 since sine is -5/6 By the Pythagorean Theorem, we know that 2 2 2 2 2 x + 5 = 6 ⇒ x + 25 = 36 ⇒ x = 11 ⇒ x = 11 So, we get the following ratios for the other 5 trig functions 11 5 6 6 cos θ = − tanθ = cscθ = − secθ = − cotθ = 6 11 5 11 11 5 The Unit Circle: The unit circle is a circle centered at the origin with radius 1, hence the name unit circle. It allows us to easily find the values of sine and cosine, and thus the rest of the trigonometric functions quickly and easily. There is a picture of the unit circle on the following page (Figure 11). The x-coordinates are the values of cosine and the y- coordinates are the values of sine. Page 8 of 23
<strong>Trigonometry</strong> Figure 11: The Unit Circle Graphs of the Trigonometric Functions: 1) f ( x) = sin x Domain of f: All real numbers x-intercepts: Let y = 0 , sin x = 0 ⇒ x = nπ where n is an integer. y-intercept: Let x = 0 , sin 0 = 0 π − 2 π 2 Figure 12: f ( x) = sin x Page 9 of 23
Page 1 and 2: Trigonometry Table of Contents: Bac
Page 3 and 4: Trigonometry Angles: 1) Standard Po
Page 5 and 6: Trigonometry The length of the arc
Page 7: Trigonometry 5) Signs The signs of
Page 11 and 12: Trigonometry Figure 17: f ( x) = co
Page 13 and 14: Trigonometry 4) Inverse Cosecant If
Page 15 and 16: Trigonometry 2 2 7) tan θ + 1 = se
Page 17 and 18: Trigonometry 7) Alternate forms of
Page 19 and 20: Trigonometry The Law of Sines In an
Page 21 and 22: Trigonometry Extra Problems 1. A ci
Page 23: Trigonometry Answers to Extra Probl

Trigonometry Handout

Create successful ePaper yourself

Delete template?

Save as template?