Question

WILL FAN AND GIVE MEDAL!

For 1-3, Find sin(2(theta)), cos(2(theta)), and tan(2(theta)) exactly.

1. Suppose that sin(theta)=3/5 and theta is in the first quadrant.

2. Tan(theta) = 12/5 and is in the third quadrant

3. Tan(theta) = (-(radical 11))/(5) and is in the second quadrant

PLEASE EXPLAIN STEP BY STEP!

Answer 1

do your notes have the "double angle" formulas ?
for example, what is the formula for sin(2x) ?

Answer 2

sin 2A = 2 sin A cos A

Answer 3

I know the formulas and they're listed on this site... http://www.regentsprep.org/regents/math/algtrig/regentsreferencesheet.pdf

Answer 4

@phi

Answer 5

for 1) they give sin(A)= 3/5
if you knew cos A, you could use your formula to find sin 2A
right ?

Answer 6

So I draw a triangle and the hypotenuse is 5, opposite is 3, and adjacent is 4.

The formula is sin 2A = 2 sin A cos A

So then it equals, 2(3/5)(4/5) = .96

Answer 7

@phi

Answer 8

yes. that is the basic idea. You will always get 2 sides of a right triangle.
use pythagoras to find the 3rd side (though 3,4,5 and 5,12,13 are very common numbers for right triangles)

Answer 9

Thank you very much for your help! You rock!

Answer 10

now use the formulas for cos 2A and Tan 2A