Transcript Do Now: #`s 79, 81, 83: part a

Academy Algebra II
13.4: Evaluate Inverse Trigonometric Functions (PC 4.7)
HW: p.878 (3-10 all, 16-24 even, 27-31 all, 35, 36)
Inverse Trig Functions
• Inverse function is denoted by:
1
y  arcsin x or
y  sin x
• arcsin x means the angle whose sine is x.
(same meaning as inverse)
Evaluate the expression without using a calc.
1
1.) (a) arccos
2
1
1 
2.) (a) cos   
 2
(b) arccos 0
(b) sin
1
2
2
Use a calculator to approximate the value.
3.) (a) arcsin( 0.75) (b) cos 1 (0.7)
4.) (a)
tan 1 0.98
(b) arctan 4.7
Use an inverse trig function to write as
a function of x.
Example:
A swimming pool is 20 meters long and 12 meters
wide. The bottom of the pool has a constant slant so
that the water depth is 1.3 meters at the shallow end
and 4 meters at the deep end. Find the angle of
depression of the bottom of the pool.
Pre-Calc book: p.353 (70)
Find the exact value of each of the remaining trig
functions of .
3
1.) cos   ,  is in Quadrant IV
5
2
2.) sin    , 180    270
3
3.) sec   2, sin   0
4.) cot   2, sec   0
Use a calculator to approximate two values of  . 0    360
1.) sin   0.8191
2.) tan   0.6524
3.) sec  1.2241
4.) cos  0.9848
PC Book: Find the two solutions of the equation.
Give your answers in both degrees
and radians.
Do not use a calculator.
1
2
79a.) sin  
80a.) cos  
2
2
2 3
81a.) csc 
3
81b.) cot  1
2 3
83a.) sec   
3
1
83b.) cos   
2
PC Book: Find the indicated trig value in the specified
quadrant.
3
97.) sin    ; Quadrant IV; Find cos 
5
98.) cot   3 ; Quadrant II; Find sin 
3
99.) tan   ; Quadrant III; Find sec 
2
100.) csc   2 ; Quadrant IV; Find cot 
Pre-Calc book: p.354 (77)
Pre-Calc book: p.312 (65)
Pre-Calc book: p.312 (68)