Find the value of Cos 220 degree.
To find values of angles more than 180 or 90 degrees we use quadrant rule. See the following quadrant angle graph to understand it,
For first quadrant i.e. angle less than 90 degrees and more than zero degree: all the trigonometry ratios are positive.
For second quadrant i.e. angle between 90 and 180 degrees sine and cosec are positive.
For third quadrant i.e. angle between 180 and 270 degrees tangent and cotangent are positive.
For fourth quadrant i.e. angle between 270 and 360 degrees cosine and secant are positive.
And if we conversion angle consist 90+, 90- or 270+, 270- we change the ratio as sine into cosine,
tan into cot,
sec into cosec.
And if conversion angle consist 180+, 180- or 360+, 360- there is no change in ratio.
For example, cos2250
Step 1: cos 225 = cos (180+45)
Step 2: As angle start with 180+, so no change in ratio. i.e. cos remains cos.
step 3: 225 angle lie between 180-270 i.e. third quadrant. In this quadrant cos is negative.
Now by following step 2 and step 3 we get,
cos 225 = -cos 45 =
Step 1: cos 225 = cos (270-45)
Step 2: Angle start with 270+ so cos will change into sine.
Step 3: angle lie in third quadrant so sine will be negative. Thus,
cos 225 = -sin 45 =