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Precalc Final Answers
This deck contains 36 flashcards covering solutions to various precalculus problems, including trigonometric identities, vector operations, and complex numbers.
Find csc x and cot x if cos x = -4/7 and sin x > 0
csc x = (7 √(33))/33
cot x = (-4 √33)/33
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Key Terms
Term
Definition
Find csc x and cot x if cos x = -4/7 and sin x > 0
csc x = (7 √(33))/33
cot x = (-4 √33)/33
When tan x =4/3 where π ≤ x ≤ 3 π/2, Find cos 2x.
-7/25
When cos x = -8/17 where π≤x≤3π/2, find cos 2x.
-161/289
Solve this eqution for 0≤x≤2π (√2)sin(x)csc(x) + 2csc(x) = 2sin(x) + 2csc(x)
x= π/4, 3π/4
Solve: cos^2(x) + 2 = 2cos(x) + 1
x = 0, 2π
0=2 tan(x) - sec^2 (x)
x = π/4 , 5π/4
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| Term | Definition |
|---|---|
Find csc x and cot x if cos x = -4/7 and sin x > 0 | csc x = (7 √(33))/33
cot x = (-4 √33)/33 |
When tan x =4/3 where π ≤ x ≤ 3 π/2, Find cos 2x. | -7/25 |
When cos x = -8/17 where π≤x≤3π/2, find cos 2x. | -161/289 |
Solve this eqution for 0≤x≤2π (√2)sin(x)csc(x) + 2csc(x) = 2sin(x) + 2csc(x) | x= π/4, 3π/4 |
Solve: cos^2(x) + 2 = 2cos(x) + 1 | x = 0, 2π |
0=2 tan(x) - sec^2 (x) | x = π/4 , 5π/4 |
-csc^2 (x) +2 = 0 | x = π/4 , 3π/4, 5π/4, 7π/4 |
cos(x) = cos 2(x) | x = 0, 2π/3, 4π/3 |
5 + sin x = (10 + √3)/2 | x = π/3, 2π/3 |
arctan (tan 3π/4) = x | x = -π/4 |
arctan (sec(π)) = x | x = -π/4 |
arccos (sin(0)) = x | x = π/2 |
arcsin (csc (π/2)) = x | x = π/2 |
Solve the triangle: c = 17 cm, a = 15 cm, b = 28 cm | angle A = 27.03 degrees
angle B = 121.96 degrees
angle C = 31.101 degrees |
Solve the triangle: angle C = 65 degrees, b = 35 yd, c = 32 yd | angle B = 82.43 degrees
angle A = 32.57 degrees
a = 19.01 yd |
Solve the triangle: angle C = 62 degrees, b = 15 mi, c = 10 mi, SSA | NO TRIANGLE |
cos ( -7π/12) | (√2 - √6)/4 |
tan (5π/12) | 2 + √3 |
u = <4,1> | Component Form: <-6,0> or -6i |
u = <4,6> | Component Form: <-8,10> |
Find the angle between the two vectors: u = -6i - 3j v = 2i - 8j | x = 77.47 degrees |
Find the angle between the two vectors: u = <7,2> v = <-6,-5> | x = 156.14 degrees |
Write the vector in component form: Vector CD where C = <0,-2> D= <1,0> | <1,2> |
Find the component form of the resultant vector: a = <9,-40> Find 2a | <18,-80> or 18i-80j |
Find the direction angle for AB where; A = <0,-5> B = <1,5> | <1,10> is the vector so the direction angle is 84.29 degrees. |
Find the dot product: u = <5,-4> v = <-3,-5> | 5 |
Find the dot product: u = - 8i - 5j v = 7i - 4j | -36 |
State if the vector is parallel, orthogonal, or neither: u = <40,-40> v = <-6,8> | neither |
State if the vector is parallel, orthogonal, or neither: u = <-12,-10> v = <5,-6> | orthogonal |
Write in trig form: -√3 + i | = 2(cos (-π/6) + i sin (-π/6)) or = 2(cos 150 + i sin 150) |
Write in trig form: √6 - 3i√2 | = 2√6 (cos 300 + i sin 300) or = 2√6 (cos π/3 + i sin π/3) |
Write in rectangular form: 4(cos 60 + i sin 60) | 2 + 2i√3 |
Write in rectangular form: 4(cos (4π/3) + i sin (4π/3) ) | - 2 - 2i√3 |
√6(cos 90 + i sin 90) x 4 (cos 120 + i sin 120) | -6√2 - 2√6 i |
√31 (cos 240 + isin 240)/ √31 (cos 210 + i sin 210) | √3/2 + i/2 |
[(3√3)/2 + 3i/2)] ^3 | 27i |