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Trigonometry is a branch of mathematics that means "measurement of, with and by means of triangles". Astronomers as early as 150 BC developed the study of trigonometry.  By about 1500 AD the trig. ratios (sine, cosine and tangent) were established.  Once again, right-angled triangles, as in Pythagoras' Theorem,  are important when making calculations with the trig ratios. Radians Conversions Before we discuss the definition of the trig ratios it is important to understand how angles are measured. You are probably used to expressing angles in degrees, but it is also possible to express angles in radians.   RADIANS A radian is the angle made when the radius of a circle represents an arc on its perimeter. OR One radian is the measure of the angle subtended at the centre of a circle by an arc equal in length to the radius of the circle.                           Usually, 1 radian is written as 1c.                                               1 radian = 57.30º Radians are often used instead of degrees in advanced calculations. Your calculator can work in radians by changing the mode of operation from DEG to RAD.

 

IMPORTANT CONVERSIONS

 

 

 

 

 

 

 

 

Examples

Changing from radians to degrees.               Changing from degrees to radians.           Convert 240º to radians.

 

 

 

 

 

 

Have a Go Problem 1 Change 102º to radians.     Problem 2

 

Practice Questions Question 1 Express the following angles in radian measure: 15º, 135º 15'  answer 0.26 radians, 2.36 radians Question 2 Convert the following radian measure to degree: 15.86 radians, 0.076 radians.   Scroll down to see answer 908.71 degrees/ 908 degrees 4 minutes, 4.35 degrees/ 4 degrees 21 minutes   Question 3 Use your calculator to change these degrees and minutes to decimal degrees. (a)   26° 6' (b)  83° 16' answer (a) 25.1 degrees (b) 83.27 degrees   Question 4 answer (a)72 degrees (b) 1.257 radians

                        

 

 

 

 

 

 

Solution 1 Change 102º to radians. back to Have a Go

Solution 2   back to Have a Go

 

 

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