Use the sum-to-product formulas to find the exact value of the given expression.
sin 150° + sin 30°
sum of sines:
sinA + sinB = 2sin( (A+B)/2) cos( (A-B)/2)
then:
sin 150° + sin 30° = 2sin 90° cos 60°
= 2(1)(1/2)
= 1
Difference of sines:
sinA - sinB = 2cos( (A+B)/2) sin( (A-B)/2)
then:
sin 4θ − sin 2θ
= 2cos(3Ø)sin Ø
To find the exact value of the expression sin 150° + sin 30° using the sum-to-product formulas, we can rewrite the expression in terms of the sum-to-product formulas.
The sum-to-product formulas state that:
sin(A) + sin(B) = 2sin((A+B)/2)cos((A-B)/2).
Using this formula, we can rewrite the expression sin 150° + sin 30° as:
2sin((150° + 30°)/2)cos((150° - 30°)/2).
Simplifying, we get:
2sin(180°/2)cos(120°/2).
Now, sin(180°/2) is equal to sin(90°) which is 1, and cos(120°/2) is equal to cos(60°) which is also 1/2.
Substituting these values, we have:
2(1)(1/2) = 1.
Therefore, the exact value of sin 150° + sin 30° is 1.
Sorry, I have figured out this one but cannot figure out this one
Use the sum-to-product formulas to write the given expression as a product. sin 4θ − sin 2θ
Could you help me with this one instead please?