Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 6.2
Page 1 / 5
Right Triangle Trigonometry
Acute Angle Trig Functions
Goal: Make sure that you can list out all 6 trig functions, and their definition as ratios of sides of a
right triangle
Given this triangle
Write out the definition of
All 6 trig functions (as ratios
of the sides )
1)
2)
3)
4)
5)
6)
7) Write out that mnemonic that your instructor told you about. Then start memorizing it!!
8) How are csc, sec, and cot related to sin, cos, and tan?
9) For each figure, calculate the values of all 6 trig ratios, using the definitions of the functions.
Page 1 / 5
Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 6.2
Page 2 / 5
10) For each figure, calculate the values of all 6 trig ratios, using the definitions of the functions.
11) Given the values of sin and cos, determine the values of the rest of the 6 trig ratios, using the definitions of the
functions.
Sin  
3
1
, Cos 
2
2
12) Write out the three reciprocal trig identities here:
13) Write out the two quotient (division) trig identities here:
14) Write out the three Pythagorean trig identities here:
Page 2 / 5
Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 6.2
Page 3 / 5
15) Given the values of sin and cos, determine the values of the rest of the 6 trig functions, using
the various trig identities (instead of the definitions/ratios of various trig functions)
sin  
3
15
16) Given the values of sin and cos, determine the values of the rest of the 6 trig functions using the various trig
identities.
sin  
3 7
7
, cos  
8
4
17) Given the values of sin and cos, determine the values of the rest of the 6 trig functions using the various trig
identities.
sin  
3
7
, cos  
15
30
18) Given the values of sin and cos, determine the values of the rest of the 6 trig functions using the various trig
identities.
sin  
3 7
7
, cos  
8
4
Page 3 / 5
Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 6.2
Page 4 / 5
19) Imagine that you're given the value of Sinθ, for some triangle. Sketch out a way, using the identities, to arrive at
all of the other trig functions. Hint: Remember that you can 'build off' of what you've already got. As in "Sweet! I was
given Sin, and now I've got Cos, so I can use both of those to get Tan!"
For each function, put all the work you did to get that function into a box, and put the name of the function at the top of
that box (so it's clear what your work is)
20) Imagine that you're given the value of Cosθ, for some triangle. Sketch out a way, using the identities, to arrive at
all of the other trig functions. Hint: Remember that you can 'build off' of what you've already got. As in "Sweet! I was
given Sin, and now I've got Cos, so I can use both of those to get Tan!"
For each function, put all the work you did to get that function into a box, and put the name of the function at the top of
that box (so it's clear what your work is)
Page 4 / 5
Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 6.2
21) Do you see a pattern?
On the calculator, find the following (make sure you’re in DEGREE mode!)
1. sin 2° and the cos 88°
2. sin 10° and the cos 80°
3. sin 35° and the cos 55°
A similar relationship holds between tan and cot, sec and csc.
22) Find the exact value without using a calculator.
cos15
sin 75
23) Find the exact value without using a calculator.
cos 72 
sin 18
24) Find the exact value without using a calculator.
1  cos2 20  cos 2 70
25) Find the exact value without using a calculator.
 
 
 
tan 35  sec 55  cos 35
Page 5 / 5
Page 5 / 5