Download Trigonometric Functions: Finding Reference Angles and Values and more Assignments Logic in PDF only on Docsity!
Values of Trigonometric Functions
Definition of Reference Angle: Let be a non-quadrantal angle in standard position. The reference angle of is the acute angle R that the terminal side of makes with the x -axis.
If is in QI, R = If is in QII, R = 180 – or – If is in QIII, R = – 180 or – If is in QIV, R = 360 – or 2 –
Don’t try to ‘memorize’ these. Use logic. Always find the difference between the angle and the positive or negative x -axis.
Find the reference angle R.
= 132 = 236 = 311 = – 120
For radian measurements, such as those below, use the following guide to help you find the reference angles.
θR θR θR θR
0 or 6.
Values of Trigonometric Functions
To Find Trigonometric Values of an Angle:
**1. Determine the quadrant where the terminal side is located
- Find the reference angle
- From the quadrant, determine if the value’s sign is + or -
- Find the value with the correct sign**
Find the exact value.
sin(135) cos(240) tan( 210 )
cos( 390 )
sin
tan 3
sin
cos
tan
csc
cot
sec
Values of Trigonometric Functions
The inverse sine, inverse cosine, and inverse tangent values on a calculator are found by using the
2 nd^ key. They are labeled sin ^1 , cos ^1 , and tan^1 and are found above the sin, cos, and tan keys.
Remember; you are given the value and finding an angle.
To Find an Angle (inverse function) Given a Trigonometric Value:
**1. Make sure your calculator is in the correct mode
- Enter the value, use the 2nd**^ **key, and the correct function key
- (If you are given a secant, cosecant, or cotangent value; first find the reciprocal of that** value using the reciprocal key, then use the 2nd^ **key and correct reciprocal function key.)
- From the angle given, find the reference angle; then use it to find all angles in the given** interval
Approximate the acute angle to the nearest a) 0.01 and b) 1'
cos = 0.3456 tan = 1.
Approximate to the nearest 0.1, all angles in the interval [0 , 360 ) that satisfy the equation.
sin = 0.4567 tan = -1.4826 sec = 1.
cos = – 0.4617 cot = 2.4586 csc = – 2.
Values of Trigonometric Functions
Approximate to the nearest 0.01 radians, all angles in the interval [0, 2 ) that satisfy the equation.
cos = 0.2314 cot = – 0.5241 csc = 1.
sin = – 0.9852 tan = 5.2683 sec = – 2.
