Trigonometric equations Trigonometry

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

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

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 3sin x°  1 = 0 4cos x°  2 = 0 5tan x°  12 = 0 5sin x° + 4 = 0 4cos x° + 3 = 0 3tan x° + 2 = 1 2tan x° - 5 = 0

Trigonometric Equations Solutions sin x° = 0·766 x = 50·0 or 130·0 cos x° = 0·565 x = 55·6 or 304·4 tan x° = 4·915 x = 78·5 or 258·5 cos x° = 0·906 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 3sin x°  1 = 0 sin x° = 13 = 0·333 . . . x = 19·5 or 160·5

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

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