1. The Sine and the Cosine
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2. T OA In a right angled triangle for a given acute angle θ θ Hypotenuse
Opposite θ
Adjacent
T OA
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3. S O H In a right angled triangle for a given acute angle θ θ
Hypotenuse
Opposite θ
Adjacent
S O H
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4. C A H In a right angled triangle for a given acute angle θ θ
Hypotenuse
Opposite θ
Adjacent
C A H
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5. The 3 Trigonometric Ratios
The Sine
The Cosine
The Tangent
Opposite
Sine
Hypotenuse x
Adjacent
Cosine
Hypotenuse x
Opposite
Tangent
Adjacent x
S O H C A H T O A
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6. Trigonometric
Practice
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7. What is the tangent of θ ? What is the tangent of a ? 5 3 4 a θ
Opposite
Adjacent 3 4
tanθ = = =
0.75
Opposite
Adjacent 4 3
tana = = ≈
1.33
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8. What is the cosine of θ ? What is the cosine of a ? 5 3 4 a θ Adjacent
Hypotenuse 4 5
cosθ = = =
0.8
Adjacent
Hypotenuse 3 5
cosa = = =
0.6
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9. What is the sine of θ ? What is the sine of a ? 5 3 4 a θ Opposite
Hypotenuse 3 5
sinθ = = =
0.6
Opposite
Hypotenuse 4 5
sinθ = = =
0.8
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10. What is tanx, sinx and cosx ?13 x 5 12
Opp
Adj 12 5
tanx = = =
2.4
Opp
Hyp 12 13
sinx = = ≈
0.923
Adj
Hyp 5 13
cosx = = ≈
0.385
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11. What is tany, siny and cosy ?
Opp
Adj 15 8
tany = = =
1.875
Opp
Hyp 15 17
siny = = ≈
0.882 17 15
Adj
Hyp 8 17
cosy = = ≈
0.471 y 8
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12. What is tanθ, sinθ and cosθ ?25 θ 7 24
Opp
Adj 24 7
tanθ = = ≈
2.43
Opp
Hyp 24 25
sinθ = = =
0.96
Adj
Hyp 7 25
cosθ = = =
0.28
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13. What is tanθ, sinθ and cosθ ?8 θ
Opp
Adj 35 8
tanθ = = =
4.375
Opp
Hyp 35 37
sinθ = = ≈
0.946 35 37
Adj
Hyp 8 37
cosθ = = ≈
0.216
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14. What is tanx, sinx and cosx ?41 9 θ 40
Opp
Adj 9 40
tanx = = =
0.225
Opp
Hyp 9 41
sinx = = ≈
0.220
Adj
Hyp 40 41
cosx = = ≈
0.976
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15. © T Madas