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Trigonometry

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**Sides and Angles Basic trigonometry is about things to do**

with the different ANGLES in a right angle triangle Look at the angle labeled OPPOSITE SIDE Opposite the angle HYPOTENEUSE Opposite the right angle ADJACENT The side next to the angle

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**Examples of labeling sides**

O = Opposite H = Hypotenuse A = Adjacent H O x A O A Another example H x

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**Ratio of sides OPP = Sine of the angle HYP ADJ = Cosine of the angle**

OPP = Tangent of the angle ADJ SIN on a calculator COS on a calculator TAN on a calculator Try working out SIN 30 on your calculator, you should get 0.5 as your answer

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**Finding a side using tangent**

Remember OPP = Tangent of the angle ADJ TAN on a calculator Example Find x Label sides (Opp, Hyp, Adj) Since we want ‘Opp’ and we know ‘Adj’, choose tan. tan 50° = OPP ADJ = x 8 8 x tan 50° = x X = 9.53cm to 3 s.f. 50° 8cm x

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**Finding a side using sine**

Remember: OPP = Sine of the angle HYP SIN on a calculator Example Find x Label sides (Opp, Hyp, Adj) Since we want ‘Opp’ and we know ‘Hyp’, choose sin sin 42° = OPP HYP sin 42° = x 12 12 x sin 42° = x X = 8.03 cm to 3 s.f. 42 ° 12cm x

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**Finding a side using cosine**

Remember: ADJ = Cos of the angle HYP COS on a calculator 71 ° 33cm x Example Find x Label sides (Opp, Hyp, Adj) Since we want ‘Adj’ and we know ‘Hyp’, choose cos cos 71° = ADJ HYP cos 71° = x 33 33 x cos 71° = x X = 10.7 cm to 3 s.f.

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**Finding the hypotenuse**

Find x Label sides Cos 21° = adj hyp Cos 21° = 9 x x x Cos 21 ° = 9 x = 9 Cos 21° x = 9.64cm (3s.f.) 21° 9cm x SOHCAHTOA

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**Finding the hypotenuse**

Find x Label sides Sin 79° = opp hyp Sin 79° = 22 x x x Sin 79 ° = 22 x = 22 Sin 79° x = 22.4cm (3s.f.) 79° 22cm x SOHCAHTOA

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**( ) Finding an angle sin x = Opp Hyp Sin x = 7 11 x = Sin 7**

Find x sin x = Opp Hyp Sin x = 7 11 x = Sin x = 39.5° (to 1 d.p.) x° 7 cm 11cm ( ) -1 Remember Sin x = OPP, Cos x = ADJ, Tan x = OPP HYP HYP ADJ

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