Graph of y sin x Max sin x

Graph of y = sin x Max sin x = 1 when x = 90° Min sin x = -1 when x = 270°

Graph of y = cos x Max cos x = 1 when x = 0° or 360° Min cos x = -1 when x = 180°

Graph of y = tan x These lines are called asymptotes and show that tan xo is undefined for 90 o and 270 o The graph of y = tan xo has no maximum or minimum values

+ve +ve –ve –ve Splitting each graph into 90 o sections, shows that each has two positive and two negative sections +ve 90 o +ve sin all 180 o –ve All Sinners Take Care tan cos 270 o 0 o 360 o

The diagram shows where the various ratios are positive 90° to 180° sin positive 180 - 90° 90 S 0° to 90° all positive A 180° 180 + 0°, 360° 360 C T 180° to 270° tan positive 270° 270 360 - 270° to 360° cos positive

tan x° = 2· 73 cos x° = -0· 571 tan-1 2 · 73 = 70° cos-1 0 · 571 = 55° 90° 180° S T A C 270° x = 70° or 180 + 70 = 250° 0°, 360° 180° S T A C 270° x = 180 - 55 = 125° or 180 + 55 = 235° 0°, 360°

Trigonometric Equations Solve the following equations, giving two values for x between 0° and 360°. sin x° = 0· 766 cos x° = 0· 565 tan x° = 4· 915 cos x° = 0· 906 sin x° = 0· 707 tan x° = 2· 050 sin x° = 0· 415 tan x° = 0· 193

Trigonometric Equations Solve the following equations, giving two values for x between 0° and 360°. cos x° = 0· 174 3 sin x° 1 = 0 4 cos x° 2 = 0 5 tan x° 12 = 0 5 sin x° + 4 = 0 4 cos x° + 3 = 0 3 tan x° + 2 = 1 2 tan x° - 5 = 0

Trigonometric Equations Solutions sin x° = 0· 766 x = 50· 0 or 130· 0 x = 55· 6 or 304· 4 tan x° = 4· 915 x = 78· 5 or 258· 5 x = 155· 0 or 205· 0 sin x° = 0· 707 x = 225· 0 or 315· 0 tan x° = 2· 050 x = 116· 0 or 296· 0 sin x° = 0· 415 x = 24· 5 or 155· 5 tan x° = 0· 193 x = 10· 9 or 190· 9 cos x° = 0· 174 x = 100· 0 or 260· 0 3 sin x° 1 = 0 sin x° = 1 3 = 0· 333. . . x = 19· 5 or 160· 5 cos x° = 0· 565 cos x° = 0· 906

4 cos x° 2 = 0 cos x° = 2 4 = 0· 5 x = 60 or 300 5 tan x° 12 = 0 tan x° = 12 5 = 2· 4 x = 67· 4 or 247· 4 5 sin x° + 4 = 0 sin x° = 4 5 = 0· 8 x = 233· 1 or 306· 9 4 cos x° + 3 = 0 cos x° = 3 4 = 0· 75 x = 138· 6 or 221· 4 3 tan x° + 2 = 1 tan x° = 1 3 = 0· 333. . . x = 161· 6 or 341· 6

Solve the following equations, giving two values for x between 0° and 360°. 2 cos x° + 1 = 0 5 sin x° 1 = 0 8 cos x° 2 = 0 5 tan x° + 8 = 0 7 sin x° + 3 = 0 10 cos x° - 9 = 0 3 sin x° + 2 = 1 4 tan x° - 15 = 0