1. Solving
Trig
Equations

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

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

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

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

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

7.     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
= 250°
x =
= 125° or
= 235°

8. 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

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

10. 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·
x = 19·5 or 160·5

11. 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·
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

12. 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 = cos x° - 9 = 0
3sin x° + 2 = 1 4tan x° - 15 = 0