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
A compound angle is an angle that is formed by adding or subtracting two or more individual angles. It is denoted as (a+b) or (a-b), where a and b are the individual angles.
To find the exact value of cos(a+b), you can use the double angle formula for cosine, which is cos(a+b) = cos(a)cos(b) - sin(a)sin(b). You will need to know the exact values of cos(a) and sin(a) to substitute into the formula.
No, a calculator can only give you an approximate value for cos(a+b). To find the exact value, you will need to use mathematical formulas and the exact values of cos(a) and sin(a).
A simple angle is an angle that is not formed by adding or subtracting other angles. It is just one single angle. A compound angle, on the other hand, is formed by adding or subtracting two or more individual angles.
Finding the exact value of cos(a+b) is important because it allows us to solve more complex trigonometric equations and better understand the relationship between different angles. It also helps us to make precise calculations in fields such as engineering, physics, and astronomy.