Find other trig functions- if cos(Θ)=0.85 what is sin(Θ)

[lucifers]

I understand that I am suppose to use the pythagoras theorem, but i am not sure how.
The answer that i am suppose to arrive at is below. Thanks!


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3

 

[MarkFL]

Hello, and welcome to FMH!

If \(\cos(\theta)=0.85\), this means \(\theta\) is either a quadrant I or quadrant IV angle (since we're given no other information about \(\theta\)). I would indeed begin with a Pythagorean identity:

[MATH]\sin^2(\theta)+\cos^2(\theta)=1[/MATH]
Can you solve this for \(\sin(\theta)\)?

 

[lucifers]

Hello, and welcome to FMH!

If \(\cos(\theta)=0.85\), this means \(\theta\) is either a quadrant I or quadrant IV angle (since we're given no other information about \(\theta\)). I would indeed begin with a Pythagorean identity:

[MATH]\sin^2(\theta)+\cos^2(\theta)=1[/MATH]
Can you solve this for \(\sin(\theta)\)?

I would imagine it would go something like this

sin2(θ)+cos2(0.85)=1

sin2(θ)=1-0.7225=0.2775

sin=0.2775


however this does not coincide with the answer that is given at the back of my math book and the fast reply and welcome is much appreciated!

 

[MarkFL]

I would first solve for \(\sin(\theta)\):

[MATH]\sin(\theta)=\pm\sqrt{1-\cos^2(\theta)}[/MATH]
Now, let \(\cos(\theta)=0.85=\dfrac{17}{20}\):

[MATH]\sin(\theta)=\pm\sqrt{1-\left(\frac{17}{20}\right)^2}=\pm\frac{\sqrt{111}}{20}\approx\pm0.52678268764263694242[/MATH]
Now, as far as this not matching the result you are expected to match, can you verify that everything is stated correctly, and the entire problem has been posted?

 

[Steven G]

I would imagine it would go something like this

sin2(θ)+cos2(0.85)=1

sin2(θ)=1-0.7225=0.2775

sin=0.2775


however this does not coincide with the answer that is given at the back of my math book and the fast reply and welcome is much appreciated!

First of all sin has no meaning so saying sin=0.2775 is meaningless. You compute sin of angles, like sin 70^o, sin 125^oand sin 7radians.
I suspect by sin2(θ) you mean sin²(2θ) or sin^2(θ). If you feel that sin²(θ)= 0.2775 then why would you think that sin(θ)= 0.2775????

 

[Dr.Peterson]

I understand that I am suppose to use the pythagoras theorem, but i am not sure how.
The answer that i am suppose to arrive at is below. Thanks!


2√3
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3

That can't be the correct answer, because it equals 1.1547, and sines and cosines can't be greater than 1! Check that you looked at the answer to the right problem.

As for the answer you got, don't forget to take the square root.

 

[Steven G]

How about sin(arccos(.85))~+/- 0.52678268764