# trigonometry

posted by .

1) Perform the operation and leave the result in trig. form.

[3/4(cos pi/3 + i sin pi/3)][4(cos 3pi/4 + i sin 3pi/4)]

Thanks

• trigonometry -

[3/4(cos pi/3 + i sin pi/3)][4(cos 3pi/4 + i sin 3pi/4)]
= (3/4)(1/2 + i (√3/2) (4) (-√2/2 + i √2/2)
= (3/4)(1/2)(1 + i √3)(4)(1/2)( -√2 + i √2)
= (3/4)(-√2 + i√2 - i √6 + √6 i^2)
= (3/4) (-√2 -√6 + i(√2-√6) ) --- in quad III

tan^-1 | √2-√6|/|-√2-√6| = 15° or π/12
but the angle is in III , so Ø = 135° or 9π/12

= (3/4)( cos 9π/12 + i sin 9π/12)

check my arithmetic, I should have written it out on paper first.

## Similar Questions

1. ### trig

Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity …
2. ### tigonometry

expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) …
3. ### Trig

Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
4. ### TRIG!

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
5. ### Pre Cal.

Express 5sqrt(3) - 5i in polar form. A: 10(cos(11pi/6) + i sin(11pi/6)) Express 4(cos(3pi/4) + i sin(3pi/4)) in rectangular form. A: -2sqrt(2) + 2sqrt(2i Write 2x+y=5 in polar form. A: sqrt(5)= r cos (theta-27degrees) Are these correct?
6. ### math

u=(2 cos pi/4)i + (2 sin pi/4)j, v = (cos 3pi/2)i + (sin 3pi/2)j find the angle theta between the two I'm at a lost on what to do.
7. ### Math

Test for symmetry with repsect to Q=pi/2, the polar axis, and the pole. r=16cos 3Q r=16cos(3pi/3 + 3h) = 16(cos3pi/2 3h- sin 3pi/2 sin h) cos 3pi/2 = 0 sin 3pi/2 = -1 Not symmetrical My teacher said that this was wrong!Why?
8. ### Math

Test for symmetry with repsect to Q=pi/2, the polar axis, and the pole. r=16cos 3Q r=16cos(3pi/3 + 3h) = 16(cos3pi/2 3h- sin 3pi/2 sin h) cos 3pi/2 = 0 sin 3pi/2 = -1 Not symmetrical My teacher said that this was wrong!Why?
9. ### trig

Solve cos x-1 = sin^2 x Find all solutions on the interval [0,2pi) a. x=pi, x=pi/2, x= 2pi/3 b. x=3pi/7, x=pi/2, x=2pi/3 c. x=3pi/7, x=3pi/2, x=3pi/2 d. x=pi, x=pi/2, x=3pi/2
10. ### Algebra 2

What values for theta(0 <= theta <= 2pi) satisfy the equation?

More Similar Questions

Post a New Question