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# AP Physics problem

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If (1.33)sin(25) = (1.5)sin(theta), what is theta?

So far, I got this:

(1.33)sin(25) = (1.5)sin(theta)

sin(theta) = (1.33)sin(25) / (-0.11735188)

I don't know what else to do... a little help? Please?

Jul 23, 2017

#1
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I do not understand how you got to $$sin(\Theta)=1.33sin(\Theta)/(-0.1135188)$$; however, this is how I would sove this equation.

$$1.33\times sin(25) = 1.5\times sin(\Theta)$$

$$1.33\times -0.132351750098 ≈ 1.5\times sin(\Theta)$$

$$-0.17602782763034 ≈ 1.5\times sin(\Theta)$$

$$\frac{-0.17602782763034}{1.5} ≈ \frac{1.5\times sin(\Theta)}{1.5}$$

$$\frac{-0.17602782763034}{1.5} ≈ \frac{1\times sin(\Theta)}{1}$$

$$\frac{-0.17602782763034}{1.5} ≈ 1\times sin(\Theta)$$

$$\frac{-0.17602782763034}{1.5} ≈ sin(\Theta)$$

$$-0.1173518850868933 ≈ sin(\Theta)$$

$${sin}^{-1}(-0.1173518850868933) ≈ {sin}^{-1}[sin(\Theta)]$$

$$-0.11762291934 ≈\Theta$$

$$\Theta≈-0.11762291934$$

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Jul 23, 2017
edited by gibsonj338  Jul 23, 2017
#2
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If (1.33)sin(25) = (1.5)sin(theta), what is theta?

1.33 x 0.42261826..... = 1.5sin(theta)

0.5620823.... = 1.5sin(theta)   divide both sides by 1.5

Sin(theta) =0.5620823 / 1.5

Sin(theta) = 0.37472152541.....

Theta = Sin^-1(0.37472152541)

Theta = 22 Degrees.

Jul 23, 2017
#3
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(1.33)sin(25) = (1.5)sin(theta)

I think if is reasonable to assume that the given angles is 25 degrees

$$(1.33)sin(25) = (1.5)sin(\theta)\\ \frac{(1.33)sin(25) }{1.5}= \frac{(1.5)sin(\theta)}{1.5}\\ sin\theta = \frac{(1.33)sin(25) }{1.5}$$

1.33*sin(25)/1.5 = 0.3747215254103533

$$sin\theta = 0.3747215254103533\\ \theta =sin^{-1}0.3747215254103533$$

asin(0.3747215254103533) = 22.007102456653

$$\theta\approx 22^\circ$$

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Jul 23, 2017