Trigonometric Ratios of Acute Angles. Rt △ ABC ∠ ACB=90° To ∠ BAC : Opposite: a=BC Hypotenuse: h=AB Adjacent: b=AC NameAbbreviationExpressionSinesina/h. - ppt download

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.

Solved 54 CHAPTER 2 Acute Angles and Right Triangles Suppose

How do you find the values of all six trigonometric functions of a right triangle ABC where C is the right angle, given a=20, b=21, c=29?

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

8.01 Trigonometric functions as right triangle ratios, Algebra 2 Math, Maryland Algebra 2 - 2020 Edition

45 ⁰ 45 – 45 – 90 Triangle:. 60 ⁰ 30 – 60 – 90 Triangle: i) The hypotenuse is twice the shorter leg. - ppt download

Right Triangle Triginometry A Stand-Alone Instructional Resource Created by Lindsay Sanders. - ppt download

Textbooks :: Mathspace

Find All Six Trig Ratios for Angle B

Warm – Up: 2/4 Convert from radians to degrees. - ppt download

11.Trigonometry ) Trigonometry is derived from Greek words tri ( three) gonon (angles) and metron ( measure). Trigonometry means the measure. - ppt download

Question Video: Using Trigonometry to Solve Right-Angled Triangles with Angles in Degrees

Section 4.3: Right Triangle Trigonometry