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Warm-Up 2/12 Evaluate – this is unit circle stuff, draw your triangle. 2 1. 1.sin 4 2 2.Cos 1 (1) 3.Tan 1 (1) Cos 1 ( 2. 3 ) 2 13 3. 12 7.1 Basic Trigonometric Identities Trig Identity: a trig expression that is true for all values of the variables Reciprocal Identities 1 sin csc 1 cos sec 1 csc sin 1 sec cos 1 tan cot 1 cot tan Quotient Identities sin cos tan cot cos sin Pythagorean Identities sin 2 cos 2 1 tan 1 sec 2 2 1 cot 2 csc2 This is the most basic all are derived from it. Divide everything by cos2 Divide everything by sin2 Opposite angle Identities sin( A) sin A cos( A) cos A Examples Use the given info to find the trig value. 3 1. If sec , find cos . 2 Since cos 2 cos 3 and sec are reciprocals, 2. If 4 csc , use the identities to find tan 3 1 cot csc 2 2 4 1 cot 3 16 2 1 cot 9 7 2 cot 9 2 2 7 cot 3 Use an identity that involves given info. Then Substitute what you know. Move the 1 to the right side. Change it to 9/9. 3 3 7 tan 7 7 Express each value as a trigonometric function of an angle in Quadrant I. 3. sin 600 sin 240 2 Subtract 360 or 2 if in radians Draw everything you know. Then draw the same reference angle in the first quadrant. 3 -1 60 3 60 1 2 negative Sine is ____________ in the 3rd quadrant So If I have to write it as an angle in the 1st quadrant will it be the same or will I have to take the opposite? Take the opposite, so your final answer is -sin60o If the original problem is in radians your final answer must be in radians, if it is degrees, your final answer will be in degrees. Try these: 19 1.sin 4 Check: 1.sin 4 2.cos(410) 2.cos50 37 3.tan 6 3.tan 6 If the original problem is in radians your final answer must be in radians, if it is degrees, your final answer will be in degrees. Simplify sin x sin x cot x 2 sin x(1 cot 2 x) 2 sin x(csc x) Is there a GCF? Yes sinx Factor Use your identities, look back at your notes 1+cot2x = csc2x 1 sin x 2 Write csc x in terms of sin x, sin x 1 sin x csc x Simplify completely done 7.1 Assignment p. 428 # 25 – 35, 45 – 53 odds Must use the identities for #25 - 35