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Trigonometry Revision Note
16/05/2023
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Trigonometry Introduction Trigonometry is another branch of maths which is all about finding the angles and sides of commonly a right- angled triangle. In a right-angled triangle, the sides are called: Opposite Hypotenuse Adjacent Hypotenuse-Longest side of the triangle Adjacent - The side which the angle connects to the hypotenuse Opposite - The remaining side of the right-angled triangle Sometimes, the angle can be placed like this: So the placement names of the sides can differ, therefore: This can sometimes be adjacent SOH CAH ТОА Always Hypotenuse This can sometimes be opposite Sine Opposite Hypotenuse Cosine Adjacent Hypotenuse Tangent Opposite Adjacent Say for Sine: Sine = o/h For Finding a side: hyp X 40° 8cm opp SOCATO Sine Rule Sin 0 =ñ Theta (Greek 8 Sin40 Sign for angle) 8 Sin e ===> =12.445 L>12.45 (round to 2d.p.) cm орр adj X 50cm SOCATA Sine Rule hyp Sin == D 60 adj Sin == For Finding an angle with Sine Rule: OR (hyp X 50 50, 50 x Sin 60 = 43.30 cm (rounded to 2 d.p.) 9 cm SiCA T₂ Sine Rule 7.4 Sinxăn Sin xe t x= ㅋ 74am Sing opp Replacing theta with x To find the angle, you would For Cosine, Cos = a/h adj Finding a side: Xx as the angle is have to do the unknown the inverse operation so doing: ५० Sin - (-7.4) = 55·31° /rounded to2 d.p. пур SC Cosine Rule Cos 0= a Cos 0= = so, OR 6x Cos 40=2.05cm (2 d.p.) opp hup SA CATA 3m 45 (adj) Cosine Rule Cos 0= a Cos 0 = 73 1.3 орр So, 1.3 x Cos 45 0.92cm (2d.p.) For finding an angle with Cosine: Кур 20cm Cos x= a Cos X= t गे SHCATO cm lady Cosine 7 So, 20 Cos-¹ (7) -69.51° /rnd. For Tangent, Tangent = o/a S пур Finding a side: 22° 18cm ladj. to 2 d.p.) X opp S&CA Tangent Rule Tan 0 = — Tan 0 = 1/2 SB₂ x 18 18 X Tan 22 = 7.27...
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Alternative transcript:
(2.d.:p) am OR hyp (odb میا зат 2.8cm OPP X hyp Fining an angle with Tangent Rule: S&CALTA Tangent Rule Tan O=å Han Đ Đe 2-8 Tan 31 4-66 (2d.p.) cm X SACA Tangent Rule в ст (adj) Tanx =å Tan x= 2/7 so, Tan ( ² ) = 26.57² (2 d. p.)