USING TRIGONOMETRIC FUNCTION VALUES OF 30 DEGREES, 45 DEGREES,AND 60 DEGREES, FIND THE EXACT VALUE OF SIN 75 DEGREES.

Answer 1

In Trig, there are Sum and Difference Formulas for sines, cosines, and tangents.

Because we want the sin(75), we need to find a way to make 75 out of 30 and/or 45 and/or 60

Since 45 + 30 = 75, we can use the Sum Formula for Sine:

sin(A+B) = sinAcosB + cosAsinB where A=45 and B=30 and A+B=75

sin(45 + 30) = sin(45) cos(30) + cos(45) sin(30)

sin(75) = [ 1 / sqrt(2) ] [ sqrt(3) / 2 ] + [ 1 / sqrt(2) ] [ 1 / 2 ]

(1)[ sqrt(3) ] (1) (1)

--------------- + ------------------------------

(2)[ sqrt(2) ] (2) [ sqrt(2) ]

since they have a common denominator, we can make a single fraction:

sqrt(3) + 1

--------------

2[sqrt(2)]

If your teacher wants you to rationalize the denominator, mult top and bottom by sqrt(2), then simplify

that answer would be

sqrt(2) + sqrt(6)

----------------------

4

I am available for tutoring to day online. Rate = $55/hour. Hope to hear from you. :-)