Math 162 Test 3 Practice Problems A

Math_162_test_3_practice_problems

Simplify the following trigonometric expressions. (sec x)(cos x)2 (sin x)2(csc x)2 - (sin x)2

(tan x)(csc x)

Verify (prove) the following identities. (tan x)(cos x) = (sin x)2(csc x) + sin x (sin x)(csc x) = 1 (csc x)2(tan x) = (csc x)(sec x) Write the following expression as a single trigonometric expression. cos(w)cos(800) - sin(w)sin(800)

Solve the following equation. 2cos x + sin (2x) = 0

Simplify the following expression: cos(2x) + sin2x Expand the following expression so that there is no subtraction in the domain of the sine function: sin( 2x – 5)

Find the approximate value of the following functions or composition of functions: tan-1 ( - 2) = arccos(sin( - 45o )) sin-1 ( - .5) = cos-1 (-1/√2 ) cos(cos-1 (.23 ))

Solve the following equations. sin(x) = -3/4 cos(x) = - .5 3tan x = 7.5 csc x = - 1.3 3cos x + 3 = 0 3cos2 x + 2cos x = 0 2cos x + 3sin (x)cos(x) = 0

Complete the following operations and give the answer in a + bi form. (2 – 3i) + (5 +7i) (5+ 7i) – (-9 – 8i) (4 – 3i)(2 +7i) (1 – 5i)(1 +5i) Convert the following complex numbers to polar (trigonometric) form. 4 + 3i 0 + 7i -3 + 5i -5 - 7i 4 - 5i Convert the following complex numbers to rectangular form. 3(cos 50o + i sin 50o) 10(cos 300o + i sin 300o) 5(cos 130o + i sin 130o) 11(cos 200o + i sin 200o) Complete the following division and give your answer in a + bi form. 3 + 4i . = 2 – 3i Express the complex numbers in trigonometric (polar) form. -5 + 4i 8 - 5i 0 - 7i Convert the complex numbers to a + bi form. 10(cos 200o + i sin 200o) 13(cos 180o + i sin180o) Let z = 4(cos 120o + i sin 120o), w = 6(cos 130o + i sin 130o) be two complex numbers. Perform the following operations and give the answer in trigonometric form with angles between 0 and 360 degrees. (z)(w) w z ____ w4 √ z ____ 5√ w (The fifth root of w.) Find (- 1 + i )1/2 =