trig

Given that sinA = 4/5 sinB = 1/2, both acute angles,
find exact values of
a. sin(A+B) b. Cos(A-B) c. Sec(A-B)

i know the addition formulas, just not sure of a good method to work out these, any help with how to work out any would be good, thanks.

Reply 1

El Matematico

sin(A + B) = sinAcosB + cosAsinB
=> sin(A + B) = 4/5*((3)^1/2)/2 + 3/5*1/2

If sinB = 1/2
=> B = Pi/6

so it is then easy to work out cosB

To work out cosA, look at the 3,4,5 triange.

Reply 2

Trangulor

Use pythagoras to find out cos A and cos B

Or use the special triangles to find out cos B

Use the compound angle formulae (expanded) and plug in your values of sin A, sin B, cos A and cos B, then leave answer in surd form/fractions

Reply 3

Scholesey

ok, cheers for your help.

Reply 4

Scholesey

1 other thing,
how would i write '1/root2 (sinx + cosx)' as a single trigonometric function.
x=theta
thanks

Reply 5

Trangulor

You mean (sinx + cosx)/root2?

Have you done functions of the type Rcos(x+a) or Rsin(x+a)? (where a is a constant angle)

Pick which function you want to use (sin or cos, it might specify in the question), and expand that function using the compound angle formulae (don't forget R). Then try and figure out what terms will give you R and a

Reply 6

El Matematico

Use asinx + bcosx = rsin(x + alpha)

Where r = (a^2 + b^2)^1/2 and alpha = arctan(b/a)

Reply 7

beccijayne

I'm stuck on the same question. I've worked out part a and b, but am confused with part c.
I tried rearranging sec(A-B) to 1/(cos(A-B)) and then put my answer from part b in. But this got me the wrong answer.
How should I have worked this out?