TRIGONOMETRY, GRADE 11 MATHEMATICS HOW TO CALCULATE TRIGONOMETRIC ANGLES

1. EVALUATING TRIGONOMETRIC
FUNCTIONS FROM 0 TO 2π
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2. 0
π/2
π
3π/2
A
S
T C
90 degrees
180 degrees
270 degrees
360 degrees
2π
Measure anticlockwise
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3. In which quadrant does x lie if sinx = 4/5, cosx = -3/5
II quadrant
On the vertical axis , cossin 
cottan 
eccossec 
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4. A
S
T C


cos)
2
sin( 
Ist quadrant


cot)
2
tan( 


eccos)
2
sec( 
π/2
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5. 

cos)
2
sin( 
II Quadrant
S


sin)
2
cos( 


cot)
2
tan( 
π/2
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6. T
III quadrant


cos)
2
3
sin( 


sin)
2
3
cos( 


cot)
2
3
tan( 
3π/2
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7. C
IV th quadrant


cos)
2
3
sin( 


sin)
2
3
cos(  

cot)
2
3
tan( 
3π/2
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8. On the horizontal axis ,
S
 sin)sin( 
2nd quadrant
 cos)cos( 
 tan)tan( 
π
tantancos,cossin,sin 
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9. 3rd quadrant
T
 sin)sin( 
 cos)cos( 
 tan)tan( 
π
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10. C
4TH QUADRANT
 sin)2sin( 
2π
 cos)2cos( 
 tan)2tan( 
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11. 2π
A
1ST QUADRANT
 sin)2sin( 
 cos)2cos( 
 tan)2tan( 
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12. Evaluate )
3
17
sin(


1020
180
3
17



0
360
720
1080
990
1020sin)1020sin( 
2
3
60sin)601080sin( 
 sin)sin( 
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13. 00000
330sec300cot240tan210cos135sin2
AS
T C
2
1
45sin)45180sin()135sin(
0
0

2
3
30cos)30180cos()210cos( 00

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Evaluate

14. AS
T C
330cot)30270tan()240tan( 00

3
1
60cot)60360cot()300cot( 00

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15. 1)
3
2
)(
3
1
(3)
2
3
(
2
1
2 
3
2
30sec)30360sec()330sec( 00

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