Question

1.)Find the exact solution algebriacally, if possible:

(PLEASE SHOW ALL STEPS)

sin 2x - sin x = 0

2.) GIVEN: sin u = 3/5, 0 < u < ï/2
Find the exact values of: sin 2u, cos 2u and tan 2u
using the double-angle formulas.

3.)Use the half-angle formulas to determine the exact values of sine, cosine, and tangent of the angle: 15° .

4.) Use the sum-to-product formulas to find the exact value of the expression:
sin 195°+ sin 105°

5.) Verify the identity algebraically:
(cos 4x - cos 2x)/2 sin 3x = -sin x


THANKS IN ADVANCE!

Answer 1

CORRECTION FOR NUMBER 2! THE PI SYMBOL DIDN'T SHOW UP.

GIVEN: sin u = 3/5, 0 < u < pi/2

AND BTW, THAT "PLEASE SHOW ALL STEPS" IS FOR EACH PROBLEM. :)
THANKS.

Answer 2

sin 2x - sin x = 0

I assume from the questions, that you are familiar with the common identities.
Also you don't state a domain, so I will asuume 0 ≤ x ≤ 2pi

2sinxcos - sinx = 0
sinx(2cosx - 1) = 0
sinx = 0 or cosx = 1/2

from sinx = 0 , x = 0,pi,2pi

from cosx = 1/2, x must be in quadrants I or IV, so x = pi/3 or x = (2pi-pi/3) = 5pi/3

#2, you should recognize the 3,4,5 triangle and since u is in the first quadrant, cos u = 4/5 and tanu = 3/4

Now use your double angle formulas to find sin 2u etc.

#3
Hint 15º = 45º - 30º

so sin15
= sin(45-30)
= sin45cos30 - cos45sin30
= √2/2(√3/2) - √2/2(1/2) = (√6 - √2)/4

always check these with a calculator
now do the cosine and the tangent in a similar way.

Answer 3

#4 hint: 195+105 = 300
195 - 105 = 90 mmmmhhhh!