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Advanced Functions
NAME ____________________
DATE __________ PER _____
Right Triangle Trigonometry
unit circle perspective
*You can look at trig functions in 2 ways
right triangle perspective
Right Triangle Definitions of Trig Functions:
(For
 as an acute angle of a right triangle.)
hypotenuse
opposite side

adjacent side
SOH – CAH – TOA
opp
sin  
hyp
adj
cos 
hyp
opp
tan  
adj
hyp
opp
hyp
sec  
adj
adj
cot  
opp
csc  
EXAMPLES:
1. Find the EXACT value of the 6 trig functions of the angle  given in the figure.
(Hint: find the missing side of the triangle first! Use the Pythagorean Theorem.)
cos  __________
sec  __________
sin   __________
csc  __________
tan   __________
cot   __________
5

12
2. Use the given trig function of the acute angle  to find the other 5 trig functions
of  .
cos  __________

sin  
3
8
tan   __________
sec  __________
csc  __________
cot   __________
3. Use the given function value to find the other 5 trig functions.
cos   __________
sec   __________
sin   __________
csc   __________
tan   5
cot   __________

4. Evaluate the trig functions by memory or by constructing appropriate right triangles.

a) csc 30
b) tan
4
5. Find the EXACT value of sin 2 45  cos 2 60 .
6. Find the EXACT value of 3 tan
7. Find the EXACT value of cos


4
4
 sec
tan

6

6
sin

 2 tan
3

3
.
.
Solving for Sides and Angles in Right Triangles
8. Find the exact value of x and r.
What if we’re not dealing with “special” angles? You can use trig to write equations to
solve for sides or angles.
9. Solve for x. Round to the nearest tenth place.
a)
b)
10. Solve for the missing angle, x. Round to the nearest whole degree.
11. Find the value of  in degrees
a) cos  
3
5
 0    90 .
Round to the nearest whole degree.
b) cot  
3
7