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.
RD Sharma Solutions for Class 9 Maths Chapter 10 Congruent Triangles Updated for 2023-24
3.1 Trigonometric Functions of an Acute Angle
Textbooks :: Mathspace
Right Angled Triangle: Explanation, Formula and solved examples
ABC is an acute-angled triangle. The external bisector of ∠BAC meets the line BC at point N. M is the midpoint of BC. P and Q are two points on AN such
Trigonometric Ratios of Acute Angles. Rt △ ABC ∠ ACB=90° To ∠ BAC : Opposite: a=BC Hypotenuse: h=AB Adjacent: b=AC NameAbbreviationExpressionSinesina/h. - ppt download
ABC is a right angled triangle in which ∠ABC = 90° and ∠ACB = 60°. BC is produced to D such that ∠ADB = 45°. If CD = 30 cm, what are the lengths of AB and BC? - srsb6vnn
Trigonometric Ratios of Acute Angles. Rt △ ABC ∠ ACB=90° To ∠ BAC : Opposite: a=BC Hypotenuse: h=AB Adjacent: b=AC NameAbbreviationExpressionSinesina/h. - ppt download
Trigonometric Ratios of Acute Angles. Rt △ ABC ∠ ACB=90° To ∠ BAC : Opposite: a=BC Hypotenuse: h=AB Adjacent: b=AC NameAbbreviationExpressionSinesina/h. - ppt download
What trig function to use when given all sides to be able to determine the angles A, B & C? - Quora
Trigonometric Ratios of Acute Angles. Rt △ ABC ∠ ACB=90° To ∠ BAC : Opposite: a=BC Hypotenuse: h=AB Adjacent: b=AC NameAbbreviationExpressionSinesina/h. - ppt download
In trigonometric ratios, the triangle is an acute angled triangle. How can you define sin 90 degrees? - Quora
If D and E are points on side AC and AB of a triangle ABC, such that AD = DE = EC =BC, then , show that , angle A : angle B = 1 : 3? - Quora
△ABC has ∠ABC = 90° and ∠ACB = 30°. If a point inside the triangle is chosen at random, what is the probability that it is nearer to AB than to AC? - Quora
ABC is a right angled triangle with angle C={ 90 }^{ o },BC=a,AC=b,CDbot AB and CD=P. Show that cfrac { 1 }{ { P }^{ 2 } } =cfrac { 1 }{ { a }^{ 2 } } +cfrac { 1 }{ { b }^{ 2 } }
