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AS-Level Mathematics | Trigonometry

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  • Corresponding values
  • sin-1(x), 180 - ans
  • cos-1(x), 360 - ans
  • tan-1(x), ans + 180
  • for all of them - after getting any two consecutive values, keep adding or subtracting 360 to get more values if needed

Question 1

Solve each equation for x in the interval 0 ≤ x ≤ 360°. Give your answers to 1 decimal place where appropriate.

a. cos x° = 0.185

b. cos x° = 0.4

c. cos x° = -0.39

d. cos x° = -0.636

e. sin x° = 0.27

f. sin x° = 0.813

g. sin x° = -0.203

h. sin x° = -0.6

i. tan x° = 0.1

j. tan x° = 1.6

k. tan x° = -0.7

l. tan x° = -3.4

Question 2

Solve each equation for x in the interval 0 ≤ x ≤ 360°. Give your answers to 1 decimal place where appropriate.

a. cos(x + 45)° = 0.9

b. cos(x + 45)° = -0.5

c. cos(x - 45)° = 0.2

d. cos(x - 60)° = 0.6

e. sin(x - 60)° = 0.5

f. sin(x + 30)° = 0.14

g. sin(x - 60)° = -0.89

h. sin(x - 30)° = -0.3

i. cos 2x° = 0.64

j. cos 2x° = -0.415

k. sin 2x° = 0.5

l. sin 2x° = -0.18

m. sin ½x° = 0.703

n. tan(x + 30)° = 1

o. tan(x - 60)° = -1.26

p. tan 2x° = -2.74

q. tan 3x° = 0.591

Trigonometric Identities

  • sin2(x) + cos2(x) = 1
  • sin(x)/cos(x) = tan(x) (use triangle)

Question 3





Trigonometric Identities

  • sin2(x) + cos2(x) = 1
  • sin(x)/cos(x) = tan(x) (use triangle)

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

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