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

  • Thread starter Thread starter xcortz
  • Start date Start date
  • Tags Tags
    Angles
AI Thread Summary
To find the exact value of cos(a+b) for angles a and b, where sin(a) = 2/5 in the second quadrant and tan(b) = 3/4 in the third quadrant, the formula cos(a+b) = cos(a)cos(b) - sin(a)sin(b) should be used. It is essential to derive the values of cos(a) and sin(b) using right triangle trigonometry, as the exact values are needed rather than decimal approximations. The discussion emphasizes the importance of understanding the definitions of sine and tangent in relation to the sides of a triangle. Participants are encouraged to show their work for better guidance in resolving their calculations. The goal is to compute cos(a+b) accurately using the derived values without relying on calculators.
xcortz
Messages
10
Reaction score
0
Member warned about posting with no effort shown

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
 
Physics news on Phys.org
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.
 

Similar threads

Changing ##\tan\frac{x}{2}## to ##\cos x## for a proof
Replies
8
Views
1K
I know ##tan 2\theta## but what is ##sin \theta##
Replies
8
Views
2K
Solving equations of the form ##a\sin\theta+b\cos\theta = c##
Replies
2
Views
2K
Find Radian Angle: Value of cos θ = -1/2, π ≤ θ ≤ 2π
Replies
1
Views
2K
Finding the exact value of cos(arcsin())
Replies
33
Views
5K
How to Find the Exact Values of Cosine and Sine of Compound Angles
Replies
2
Views
2K
Finding Angle C in an ABC Triangle
Replies
19
Views
3K
Finding coincident angle between 2 equally spaced sets
Replies
1
Views
1K
Why Is My Argument Calculation for Complex Number Incorrect?
Replies
14
Views
2K
How Accurate Are These Trigonometry Compound Angle Calculations?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top