The problem involves finding the exact value of cos(a+b) given that angle a is in the second quadrant with sin a = 2/5 and angle b is in the third quadrant with tan b = 3/4. The context is trigonometric identities and the application of the cosine addition formula.
Participants are engaged in clarifying the problem and exploring the necessary values for sin(a) and cos(b). Some guidance has been offered regarding the interpretation of the given values, but there is no explicit consensus on the next steps.
There is confusion regarding the interpretation of the trigonometric values provided, with participants emphasizing the need to correctly understand the definitions and relationships in trigonometry without relying on calculators.
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
cos(a+b)=cosacosb-sinasinbRay Vickson said:Check your formula in (2.) carefully.
xcortz said:cos(a+b)=cosacosb-sinasinb
They want an exact value, not a decimal answer. I don't know what the exact value is for sin2/5 or tan3/4Ray Vickson said:OK, so what is preventing you from applying that?
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
Because when I plugged the numbers in and solved for an exact value, I got 12.32/5 and it was wrong apparentlyRay Vickson said:Why do you think you need to know those values? Read the question again, carefully.
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
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).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