Thread: Trigonometric identity - HELP please

4)Given that sin 55degrees = 0.819 and cos20degrees = 0.94,
show how you would use the identities for sin(A+B) and cos(A+B) to find the following:

a) tan 35 degrees
Showing the steps you would follow. NOTE: sin^2theta+cos^2theta=1

Originally Posted by GAVREED2

4)Given that sin 55degrees = 0.819 and cos20degrees = 0.94,
show how you would use the identities for sin(A+B) and cos(A+B) to find the following:

a) tan 35 degrees
Showing the steps you would follow. NOTE: sin^2theta+cos^2theta=1

First of all, use the Pythagorean Identity to find sin(20) and cos(55).

Then remember that tan(35) = [sin(35)]/[cos(35)]

= [sin(55 - 20)]/[cos(55 - 20)]

Now use the angle sum rule to finish.

I'm not entirely sure why they want you to use the angle sum identities, since there is a shorter way. The denominator cos(35) equals sin(90-35) = sin(55), which is given.

Likewise, the numerator sin(35) = cos(90-35) = cos(55), which is known after using the Pythagorean identity.