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TRIGONOMETRY REVIEW 1.4, 1.5, 5.1-5.4 NAME: _______________________________ Use sum and difference identities to find an exact value for each of the following. 1. sin ( 75°) 4. sin 40°cos50° + cos 40°sin50° 2. cos15o ⎛ 11π ⎞ sin ⎜ ⎟ ⎝ 12 ⎠ 3. 5. cos 20° cos 40° − sin 20° sin 40° 6. sin 5π π 5π π cos + cos sin 12 4 12 4 Solve each problem below. 7. Find the six trig function values of an angle β if sin β = − 9 40 and cos β = . 41 41 9 41 40 cos β = 41 sin β = − tan β = 8. Find the six trig function values of an angle γ if csc γ = − csc β = sec β = cot β = 9 and γ is in quadrant III. 7 sin γ = csc γ = − cos γ = sec γ = tan γ = cot γ = 9 7 9. Given: cos a = − space for triangles: 60 and a is in quadrant II 61 sin b = a) sin(a + b) , b) cos(a + b) d) sin(a − b) e) 10. Given: cos a = space for triangles: a) sin(a − b) 7 and b is in quadrant I. Find 25 c) tan ( a + b ). cos( a − b) 2 and a is in quadrant IV 3 sin b = e) tan( a − b ) 9 and b is in quadrant II. Find 41 b) cos( a − b) Prove the following Identities 11. cos(360° − θ ) = cosθ 13. cos( x + y ) = cot x − tan y sin x cos y 12. cot θ + tan θ = cscθ secθ 14. cot θ tan θ + tan 2 θ = sec 2 θ STUDY YOUR RECIPROCAL, QUOTIENT and PYTHAGOREAN ANGLE IDENTITIES and THE UNIT CIRCLE