Download Trigonometric Ratios 2

LESSON 4: TRIGONOMETRIC RATIOS II
Learning Outcome:

To relate the trigonometric ratios to the coordinates of points in the unit circle

To determine exact and approximate values for trigonometric ratios

To identify the measures of angles that generate specific trigonometric values

To solve problems using trigonometric ratios
You can determine approximate values for sine, cosine, and tangent using a calculator. Most
calculators can determine trigonometric values for angles measured in degrees or radians. You
will need to set the mode to the correct angle measure.
Check:
Cos 60˚=0.5 (degree mode)
Cos 60 = -0.952412980 (radian mode) (To use radians to comply with cast rule the 60
degrees needs to be converted to radians, use cosine π/3 = 0.5)
Your calculator can also compute trigonometric ratios for negative angles. However, you should
use your knowledge of reference angles and the CAST rule to check that your calculator display
is reasonable.
Cos (-200˚) = -0.939692620…
Why is this value negative? In what quadrant does the angle terminate?
You can find the value of trigonometric ratio for cosecant, secant, or cotangent using the correct
reciprocal relationship:
sec 3.3 =
1
= −1.0127
cos 3.3
Ex. What is the approximate value for each trigonometric ratio. Round your answers to four
decimal places. Be sure to state the quadrant the angle terminates in and why the value is
positive or negative.
a. sin 1.92
b. tan (-500˚)
c. sec 85.4˚
d. 𝑐𝑜𝑠
7𝜋
5
How can you find the measure of an angle when the value of the trigonometric ratio is given?
If sin θ = 0.5, what is the measure of it’s angle?
1
Note: 𝑠𝑖𝑛−1 ≠ 𝑠𝑖𝑛𝜃
The inverse calculator keys return one answer only, when there are often two angles with the
same trigonometric function value in any full rotation. In general, it is best to use the reference
angle applied to the appropriate quadrants containing the terminal arm of the angle.
Ex. Determine the measures of all angles that satisfy each of the following.
a. cos θ = 0.843 in the domain 0° ≤ 𝜃 < 360°. Give approximate answers to the nearest
tenth.
b. sin θ = 0 in the domain 0° ≤ 𝜃 ≤ 180°. Give exact answers.
c. cot θ = -2.777 in the domain −𝜋 ≤ 𝜃 ≤ 𝜋. Give approximate answers.
d. 𝑠𝑒𝑐𝜃 =
2
√3
𝑖𝑛 𝑡ℎ𝑒 𝑑𝑜𝑚𝑎𝑖𝑛 − 2𝜋 ≤ 𝜃 ≤ 2𝜋. Give exact answers.
Assignment: pg. 202-205 #2, 7, 9-17