1. 3.7 Evaluating Trig Functions

2. Ex 1) Find the value (round to 4 dec. places)
To properly evaluate trig ratios on our calculator, we need to make sure we are in the right MODE – Degrees or Radians
If it has a degree symbol  put in Degree Mode
If no symbol at all  put in Radian Mode
Ex 1) Find the value (round to 4 dec. places)
a) cos 275°
(degree mode)
cos 275° =
b) sin (–1.4π)
(radian mode)
sin (–1.4π) =
c) tan 2
(radian mode)
tan 2 = –2.1850

3. Ex 2) Find the value (round to 4 dec. places)
To evaluate ratios when given Deg-Min-Sec, either convert to just degrees or use the °, ʹ, ʺ buttons on your calculator
To evaluate csc x, sec x & cot x, you will need to utilize the fact that they are reciprocal functions
Remember:
Ex 2) Find the value (round to 4 dec. places)
a) sec 146°
(degree mode) OR
b) cot 39° 52ʹ 15ʺ
(degree mode)

4. We can also solve for an angle (in degrees or radians) if we know the ratio. Use the inverse trig functions (sin–1θ, cos–1θ, tan–1θ)
*Often these problems can have more than 1 answer – you need to think and draw a sketch!!
Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to nearest tenth)
(degree mode!!)
a) sin θ = θ θ
θ = sin–1(0.7193)
θ = 46.0°
AND…
sinθ is (+) in QI & QII
180 – 46 = 134.0°
θ = 46.0° and 134.0°

5. Ex 3) Find the values of θ where 0° ≤ θ < 360° (round to nearest tenth)
(degree mode!!)
b) tan θ = –0.2309
θ = tan–1(–0.2309)
θ = –13.0°
13.0°
–13.0°
tanθ is (–) in QIV & QII
180 – 13 = 167.0°
360 – 13 = 347.0°
θ = 167.0° and 347.0°

6. Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest hundredth)
(radian mode!!)
a) cos θ = –0.4611
θ = cos–1(–0.4611)
θ = 2.05
2.05
–2.05
cosθ is (–) in QII & QIII
2π – 2.05 = 4.23
θ = 2.05 rad and 4.23 rad

7. Ex 4) Find the values of θ where 0 ≤ θ < 2π (round to nearest hundredth)
(radian mode!!)
b) sec θ =
1.45
–1.45
cosθ is (+) in QI & QIV
2π – 1.45 = 4.83
θ = 1.45 rad and 4.83 rad

8. Homework
#307 Pg 163 #1–41 odd, 44