sin(90°-α)=cosα cos(90°-α)=sinα tan(90°-α)=cotα cot(90°-α)=tanα sinα /cosα =tanα sin 2 α+cos 2 α=1 sinα =tanα ·cosα cosα =cotα ·sinα cotα =cosα ·cscα tanα ·cotα =1 Connections
Trigonometric Ratios of Acute Angles
Rt △ ABC ∠ ACB=90° To ∠ BAC : Opposite: a=BC Hypotenuse: h=AB Adjacent: b=AC NameAbbreviationExpressionSinesina/h Cosinecosb/h Tangenttana/b Cotangentcotb/a Secantsech/b Cosecantcsch/a
Example 1. Rt △ ABC ∠ ACB=90° BC=6 AB=10 sin ∠ B= cos ∠ B= tan ∠ B=
AC= ( )=8 AC= ( )=8 sin ∠ B= = = sin ∠ B= = = cos ∠ B= = = cos ∠ B= = = tan ∠ B= = = tan ∠ B= = = 6 10
Example 2. 0°< α <90° sin α = 0°< α <90° sin α = cos α = cos α =
Fold the △ CDE along CE ， point D is just on AB. Calculate the value of tan ∠ AFE..
∵ AB ＝ 10, rectangle ABCD ∴ DC=10 ∴ FC=10 ∵ FC=10,BC=8,Rt △ FCB ∴ FB=6 ∴ AF=4 If AE=x ∵ AE+ED=8, ED=EF ∴ AE+EF=8 ∴ EF=8-x ∴ x =(8-x) 2 ∴ x=3 ∴ AE=3 ∴ tan ∠ AFE=AE/AF=3/4
Square sin 2 α +cos 2 α =1 cos2 α =cos 2 α -sin 2 α =1-2sin 2 α =2cos 2 α- 1 sin2 α =2sin α cos α tan 2 α +1=1 / cos 2 α 2sin 2 α =1-cos2 α cot 2 α +1=1 / sin 2 α =1-2sin 2 α =2cos 2 α- 1 sin2 α =2sin α cos α tan 2 α +1=1 / cos 2 α 2sin 2 α =1-cos2 α cot 2 α +1=1 / sin 2 α Product sin α =tan α× cos α cos α =cot α× sin α tan α =sin α× sec α cot α =cos α× csc α sec α =tan α× csc α csc α =sec α× cot α Reciprocal tan α× cot α =1 sin α× csc α =1 cos α× sec α =1 Quotient sin α/ cos α =tan α =sec α/ csc α cos α/ sin α =cot α =csc α/ sec α
Rt △ ABC ，∠ C=90°, cosA=1/2, ∠ B=. 3. Rt △ ABC ，∠ C=90°, BC=a, c=___. (A)c=a sinA (C)c=b tanA (B)c=a/sinA (D)c=a/cosA A 30 B.
American Board
Trigonometric Ratios of Acute Angles. Rt △ ABC ∠ ACB=90° To ∠ BAC : Opposite: a=BC Hypotenuse: h=AB Adjacent: b=AC NameAbbreviationExpressionSinesina/h. - ppt download
3. Trigonometry Lesson 1 - Example 1
Solved CHECK Your Understanding 1. Given AABC, state the six
10/25/18 Trig-ratios – Noah Lozano Geometry Blog
45 ⁰ 45 – 45 – 90 Triangle:. 60 ⁰ 30 – 60 – 90 Triangle: i) The hypotenuse is twice the shorter leg. - ppt download
Warm – Up: 2/4 Convert from radians to degrees. - ppt download
ANSWERED] What is TRIGONOMETRY TRIGONOMETRIC RATIOS A b C a B Each - Kunduz
SOLVED: Two students describe the sides of right triangle ABC in relation to angle B. Tomas says that AB is the hypotenuse, AC is the opposite side, and BC is the adjacent
Triangle A B C is shown. Angle C A B is a right angle. Angle A B C is 30 degrees and angle B C A is 60
In triangle ABC, AC = BC and angle ACB = 90 degrees. Points P and Q are on AB such that P is between A and Q and angle QCP = 45
Trigonometric Ratios of Acute Angles. Rt △ ABC ∠ ACB=90° To ∠ BAC : Opposite: a=BC Hypotenuse: h=AB Adjacent: b=AC NameAbbreviationExpressionSinesina/h. - ppt download
If A, B and C are interior angles of a triangle ABC, then show that sin [(B + C)/2] = cos A/2. - GeeksforGeeks
