Math qeustions, help plz?

Question

The expression sqrt3 cos x + sin x = 1 is equivalent to
(a) sin(60 - x) = 0.5
(b) cos(60 + x) = 0.5
(c) sin(60 + x) = 0.5
(d) cos(45 + x) = 0.5
(e) sin(45 + x) = 0.5

Which one of those is the answer? show me steps plz

thanks

Answer 1

Since they all have 0.5 on the right, the first step is to divide through by 2:

√3 cos x + sin x = 1
<=> (√3 / 2) cos x + (1/2) sin x = 1/2
We could use 30° or 60° here, but the answers only give us 60° and 45°, so express in terms of cos 60° and sin 60°:
<=> (sin 60°) cos x + (cos 60°) sin x = 1/2
Now use the addition formula for sines:
<=> sin (60° + x) = 1/2

So the answer is (c).

Answer 2

sqrt3 cos x + sin x = 1
sin (s + t) = sin s cos t + cos s sin t
(1/2)sqrt3 cos x + (1/2)sin x = 1/2
sin60°cos x + cos60°sin x = 1/2
sin(60° + x) = 0.5

Answer 3

the 1st answer is authentic, and that i will inform you intimately why. you will use an algebraic equation to remedy. all of us comprehend that it is $a million.70 in line with pound, and we are searching for out how a lot replaced into offered with $.sixty 8. So, you write your formula like this... $a million.70 / a million lb = $0.sixty 8 / x lb (write those fractions top down, it is a few thing OVER some thing) you're searching for x, the pounds to procure. and probably you're questioning how can those be equivalent? they are equivalent because of fact they are equivalent ratios! besides, as quickly as you have your equation, flow multiply. so which you presently have: a million.70x = 0.sixty 8 (leaving the gadgets out so it is much less demanding to confirm here) x = 0.sixty 8 / a million.70 x = ?? (you will desire to be waiting to locate the answer now.) and do not forget your gadgets when you're executed. :)

Answer 4

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