Lab Questions

Mathematics

Santa Monica College

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MATH 113 PRECALCULUS II LAB 6: PRACTICE 5.2 – 5.5 Name: __________________________ Date Due: ______________ 5.2 Sum and Difference Formulas 1. Verify that the equation given is not an identity by showing that each side results in a different value. In other words, find the exact value of the left side using sum/difference formulas and then compare the result to whatever you quickly evaluate the right side to be. 2 3  2 3  sin     sin  sin 4  3 4  3 2. 13  5  13  Utilize sum/difference formulas to find the exact value of sin   given that 12  4  6 .  12  1 3. Find the exact value of cos( +  ) given that sin = 3/4 and cos = 5/13 where both  and  are in quadrant II. Draw TWO diagrams to assist, one each showing  and . 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas 4. Find the exact value of the cos(2 ) using the given figure: 4 5 5.  Find the exact value of sin(2 ) given that cos = 2/7 and /2 ≤  ≤ . Draw a diagram to assist. 2 6. Find the exact value of the tan( /2) using the given figure: 8 15  7. Find the exact value of sin( /2) given that csc = 5/3 and  ≤  ≤ 3/2. Draw a diagram to assist. 8. Rewrite cos4x in terms of the first power of cosine. This is lengthy procedure for which you should follow your notes from class closely. 3 5.4 Product-to-Sum and Sum-to-Product Formulas 9. Rewrite the product as a sum/difference, then evaluate to find the EXACT result (no decimals): 4cos 10. 7 17 cos 12 12 5  6 is NOT an identity. In other words, find the exact value of  cos  cos 12 12 12 the left side using sum-to-product formulas and then compare the result to whatever you quickly evaluate the right side to be. Show that cos . 5.2 – 5.4 Verifying Identities 11. Verify the identity algebraically: a. sin  3  x   sin x 4 b.   1  tan x tan   x   4  1  tan x c. cos 3x  cos x   tan 2 x sin 3x  sin x 5.5 Trigonometric Equations 12. Solve the exact value solutions of the equation in the interval [0, 2) a. 2sinx – 1 = 0 5 b. sin2x + 2cosx =  2 c. 4cos2x – 3 = 0 d. 2sin(2 x)  2  0 (Hint: You will need an identify here!) 6 ...
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