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CH. 4 – TRIGONOMETRIC FUNCTIONS 4.3 – Right Triangle Trig SOH CAH TOA!!! Recall your right triangle trig facts: opp sin hyp adj cos hyp opp tan adj Ex: Find the exact values of the six trig functions of θ. cos θ = 4/5 sec θ = 5/4 Use Pythagorean Theorem! Opposite side = 3 sin θ = 3/5 tan θ = 3/4 csc θ = 5/3 cot θ = 4/3 5 3 4 SOH CAH TOA!!! Ex: Find the exact values of the six trig functions of θ if sinθ = 5/6 and 0 < θ < 90°. Draw a right triangle and label known information! sin θ = 5/6 csc θ = 6/5 Use Pythagorean Theorem to find the third side! Leave it in reduced radical form! 11 cos 6 5 5 11 tan 11 11 6 6 11 sec 11 11 11 cot 5 5 6 11 IF 8 sin 17 , WHAT TRIG FUNCTION WILL GIVE A VALUE OF 1. tanθ 2. cotθ 3. cosθ 4. cscθ 5. secθ 15 ? 8 tan 2 , WHAT TRIG FUNCTION WILL GIVE A VALUE OF 5 ? IF 1. sinθ 2. cotθ 3. cosθ 4. cscθ 5. secθ IF 1. 2 sin , FIND THE cos 5 3 5 2. 3. 29 5 4. 5. 5 2 . 21 2 21 5 0% 0% 0% 0% 0% 3 IF sin , FIND THE csc 6 1. 33 6 2. 3. 99 3 6 3 4. 5. . 2 3 6 3 0% 0% 0% 0% 0% IF 1. sec 3 , FIND THE tan 2 2 2. 3. 2 2 4. 5. . 3 2 2 2 3 2 4 0% 0% 0% 0% 0% 7 IF cot , FIND THE csc 9 1. 2. 3. 4. 5. 74 7 . 88 9 2 22 9 2 154 7 9 22 2 0% 0% 0% 0% 0% TRIG IDENTITIES!!! Ex: Use trig identities to verify the equation: cos tan sin You’re being asked to prove this equation is true, so work one side out until it looks like the other side. Tip: Work out the more complex side! Strategy #1: Convert everything to sin and cos cos tan sin sin cos cos sin sin TRIG IDENTITIES!!! Ex: Use trig identities to verify the equation: (1 sin )(1 sin ) cos 2 Strategy #2: Make a substitution using the identity sin2 θ + cos2 θ = 1 (1 sin )(1 sin ) 1 sin 2 cos 2 cos 2 1 sin 2 sin 2 cos 2 sin 2 1 1 4 Find the 6 trigonometric functions for 3 . sin cos 3 2 csc 2 3 1 2 sec 2 3 3 2 tan 1 2 3 cot 1 3 2 3 3 2 13 Find the 6 trigonometric functions for 6 2 2 . 1 csc cos 0 sec sin tan 1 0 undefined cot 1 undefined 0 1 0 Find the 6 trigonometric functions for some angle θ in the 1st quadrant. csc 3 5 5 cos 2 3 sec 3 2 tan 5 2 cot 2 5 5 sin 5 3 Find the 6 trigonometric functions for some angle θ in the 2nd quadrant. sin cos 1 5 csc 5 2 6 5 1 tan 2 6 6 12 sec 5 5 6 12 2 6 cot 2 6