Contents

Basic Identities

Second Degree Identities

Simple Equations

Second Degree Equations

Quiz 

Trigonometry Main Page

Simple Equations

Consider the equation 4 sin x = tan x , range is 0° x  360°. Two ratios are involved, each of the first degree. Replace tan x by sin x/ cos x, the equation can be factorised and reduced to two simple equations.

4 sin x - tan x = 0

4 sin x - sin x/ cos x = 0

sin x(4 - 1/cos x) = 0

sin x = 0     or  4 - 1/cos x = 0

cos x = ¼

basic angle = 75.52°

x = 0°, 75.5°, 180° or 284.5° (1d.p.)

Example 2

Given that the domain is 0° x  360°, find all the angles satisfying the equation cot (2x + 10°) = -0.5

cot (2x + 10°) = -0.5

tan (2x + 10°) = -2

basic angle = 63.43°

10° 2x + 10° 730°

2x + 10° = 116.57°, 296.57°, 476.57° or 656.56°

x = 57.8°, 143.3°, 233.3° or 323.3°