2.3 Finding Trig Function Values Using a Calculator

** Make sure calculator in Degree Mode if θ is in degrees**

(To check the mode: Find sin 90^o and should get = 1)

Most calculator values are approximate because exact values are irrational and therefore cannot be represented as exact decimal values.

Approximate versus Exact Trig Values

Find cos 30^o as an exact value

Find cos 30^o as an approximate value with calculator

Summary

Exact: cos 30^o Approximate: cos 30^o

Use a calculator to find an approximate value for each:

a) tan 68^o 43’

b) cos 193.622^o

Finding secant, cosecant and cotangent

There are no calculator keys for these so must use reciprocals

(Do NOT use - these find angle values – not Trig functions)

a)

b) sec(-387^o)

Reverse Process - Find Angle values using the calculator

Use to find the angle.

Find an angle θ to nearest hundredth in [0^o , 90^o] for which

a) cos θ = .,8211754955

b) tan θ = 3.7183

If finding angle for secant, cosecant or cotangent,

First find the reciprocal of the trig value,

then find the angle

Find an angle θ to nearest hundredth in [0^o , 90^o] for which

a) cot θ = 1.4466474

b) sec θ = 1.555723827

Summary - Be very careful of proper sequence of keys to press!!

tan 12^o

sec 41^o

sin θ = .7162

csc θ = 2.8716

Application

Grade Resistance is the force experienced by an automobile as it travels uphill or downhill on a high way. This force is modeled by the equation,

F =W sin θ

where θ is the grade and W is the weight of the automobile. If the automobile is moving uphill, then θ > 0^o; if downhill, then θ < 0^o.

a) Calculate F to the nearest 10 lb for a 5500-lb car traveling an uphill grade

with θ = 3.9^o

b) Calculate F to the nearest 10 lb for a 2800-lb car traveling a downhill

grade with θ = -4.8^o

c) A 2400-lb car traveling uphill has a grade resistance of 288 lb. What is the

angle of the grade – to nearest hundredth?