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

[xcortz]

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

 

[Ray Vickson]

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.

 

[xcortz]

Check your formula in (2.) carefully.

cos(a+b)=cosacosb-sinasinb

 

[Ray Vickson]

cos(a+b)=cosacosb-sinasinb

OK, so what is preventing you from applying that?

 

[xcortz]

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

 

[Ray Vickson]

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.

 

[xcortz]

.

 

[xcortz]

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

 

[Ray Vickson]

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.

 

[Mark44]

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).

 

[stardust]

Think about what sine represents in terms of sides of triangle.