Compound Angles: Find Exact Value of cos(a+b)

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SUMMARY

The discussion focuses on finding the exact value of cos(a+b) given sin(a) = 2/5 for angle a in the second quadrant and tan(b) = 3/4 for angle b in the third quadrant. The correct formula to use is cos(a+b) = cos(a)cos(b) - sin(a)sin(b). Participants emphasize the importance of understanding the trigonometric identities and the values of sine and cosine derived from the given conditions, rather than relying on decimal approximations.

PREREQUISITES
  • Understanding of trigonometric identities, specifically the cosine addition formula.
  • Knowledge of right triangle trigonometry to derive sine and cosine values.
  • Familiarity with the unit circle and the properties of angles in different quadrants.
  • Ability to manipulate algebraic expressions involving trigonometric functions.
NEXT STEPS
  • Learn how to derive cosine and sine values from given trigonometric ratios.
  • Study the unit circle to understand the signs of trigonometric functions in different quadrants.
  • Practice using the cosine addition formula with various angle pairs.
  • Explore right triangle trigonometry to solidify understanding of sine and cosine relationships.
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Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to improve their problem-solving skills in trigonometric equations.

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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
 
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xcortz said:

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.
 
Ray Vickson said:
Check your formula in (2.) carefully.
cos(a+b)=cosacosb-sinasinb
 
xcortz said:
cos(a+b)=cosacosb-sinasinb

OK, so what is preventing you from applying that?
 
Ray Vickson said:
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
 
xcortz said:
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.
 
.
 
Ray Vickson said:
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 apparently
 
xcortz said:
Because when I plugged the numbers in and solved for an exact value, I got 12.32/5 and it was wrong apparently

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
xcortz said:
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
Think about what sine represents in terms of sides of triangle.
 

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