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Compound Angles?

  • Thread starter xcortz
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  • #1
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Homework Statement


Angle a is located in the second quadrant where sin a=2/5 and angle b is located in the third quadrant where tan b=3/4. Determine an exact value for cos(a+b) and where it is located.

Homework Equations


cos(a+b)=cosacosb+sinasinb

The Attempt at a Solution


I don't know what I'm doing
 

Answers and Replies

  • #2
Ray Vickson
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Homework Statement


Angle a is located in the second quadrant where sin a=2/5 and angle b is located in the third quadrant where tan b=3/4. Determine an exact value for cos(a+b) and where it is located.

Homework Equations


cos(a+b)=cosacosb+sinasinb

The Attempt at a Solution


I don't know what I'm doing
Check your formula in (2.) carefully.
 
  • #3
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Check your formula in (2.) carefully.
cos(a+b)=cosacosb-sinasinb
 
  • #4
Ray Vickson
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cos(a+b)=cosacosb-sinasinb
OK, so what is preventing you from applying that?
 
  • #5
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OK, so what is preventing you from applying that?
They want an exact value, not a decimal answer. I don't know what the exact value is for sin2/5 or tan3/4
 
  • #6
Ray Vickson
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They want an exact value, not a decimal answer. I don't know what the exact value is for sin2/5 or tan3/4
Why do you think you need to know those values? Read the question again, carefully.
 
  • #7
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.
 
  • #8
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Why do you think you need to know those values? Read the question again, carefully.
Because when I plugged the numbers in and solved for an exact value, I got 12.32/5 and it was wrong apparantly
 
  • #9
Ray Vickson
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Because when I plugged the numbers in and solved for an exact value, I got 12.32/5 and it was wrong apparantly
Let me repeat: read the question carefully, and show your work. We cannot tell where you are going wrong if we cannot see the details of what you have done.
 
  • #10
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They want an exact value, not a decimal answer. I don't know what the exact value is for sin2/5 or tan3/4
These value are not correct. It's not sin(2/5) -- it's sin(a) = 2/5, and similar for angle b. You are given that sin(a) = 2/5. Using right triangle trig, you should be able to find the exact value for cos(a) (don't use a calculator), and similarly for sin(b) and cos(b).
 
  • #11
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Think about what sine represents in terms of sides of triangle.
 

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