Adding Sine and Cosine

Here we are going to see the article as adding sine and cosine, generally sine and cosine are trigonometric functions it is used for measuring the side length and angle of the right angle triangle .Sine is defined as the ration of the opposite side to the hypotenuse and cosine is defined as the ratio of the adjacent side to the hypotenuse. So here the right angle triangle will be given with the corresponding sides name like adjacent, opposite and hypotenuse.

Example 1-adding Sine and Cosine:

Sin 45 +cos 45

Solution:

We know that the value of sin 45 and cos 45 (both are equal) =1/`sqrt 2` , plug these values into above expression.

`1/sqrt 2` +`1/sqrt2`

If the denominators of both fractions are same so we add the numerator part only we get the answer.

`(1+1)/sqrt 2 =2/sqrt 2`

Example 2-Adding sine and cosine:

Sin260+cos260

Solution:

Already we know that the formula for sin2 A+cos 2A=1

Here the value of A=60 so we use the formula as Sin260+cos260=1.

It will be check with the another method,

We know that the value of sin 60 is sqrt `3/2 ` and cos 60 is `1/2` plug these values into above expression

`(sqrt(3)/2)^2 + (1/2)^2` =`3/4` +`1/4` =1

We get the same answer in both the method.

Example 3-adding Sine and Cosine:

Sin 30+cos 90

Solution:

We know that the value of sin 30 and cos 90 the value of sin 30 is `1/2` and cos 90 is 0plug these values into above expression.

`1/ 2` +0= `1/2`



Example 4-Adding sine and cosine:

Sin 0+cos (-30)

Solution:

We know that the value of sin 0 is 0 and cos (-30) =cos 30 value of cos 30 is sqrt 3/2

0+`(sqrt3)/2` =`(sqrt 3)/2.`

Practice problem -Adding sine and cosine:

1)    Add sin2 25+cos2 25

Answer =1

2)    Add sin 67+cos 13

Answer =1.8949