Download Section 2_1 - Acute Angles and Right Triangles

Section 2.1 – Acute Angles and Right Triangles Right Triangle based definitions of the trigonometric functions: sin A=

csc A=

cosA=

secA=

tan A=

cotA=

Mnemonic to help remember: S O H C A H T O A Find the values of the 6 trig functions for the given angle: Ex1: B sin A=
cscA=
cosA=
secA=
tanA=
cotA=
C 28 45 A
53 sin B=
cscB=
cosB=
secB=
tanB=
cotB=
Notice that: sin A= tanA= sec A= Because the non‐right angles in our right triangle must add up to 90 we can then say: COFUNCTION IDENTITIES: 
sin A=cos 90  A


tanA=cot 90  A


secA=csc 90  A


cosA=sin 90  A


cotA=tan 90  A


cscA=sec 90  A

Write the function in terms of its cofunction: Ex2: cot 73 



Ex3: cos   20 Solve for the angle in the following equations: Ex4: cos   sin 2 

Ex5: sec   10  csc 2   20 Find the unknown side length using Pythagorean Theorem and then find the values of the six trig functions for angle B A
sin B=
cscB=
Ex7: a=3 b=5 cosB=
secB=
tanB=
cotB=
B C Recall that the largest side of a triangle is across from the largest angle. Knowing this information can help us compare the value of trig functions Determine whether the statement is TRUE or FALSE Ex9: sin 72  cos 72 Ex8: sin 50  sin 40 Trig Function Values of special angles: 30 , 45 , 60 30 , 60 45  sin  cos  tan  csc  Ex10: Find the exact value of each labeled part of the triangle 45° 24 d b 60° a c sec  cot 