How can I find the exact value of 4cos(7ð/4)-2sin(ð/3)?
In a graphic calculator punch in cos(7/4) and should give you the right answer
subtract it from sin(0/3)
and tada!
the weird symbol is suppose to be pi (3.14...) not a zero. it got messed up after submitting the question
need to show my work
4cos(7π/4)-2sin(π/3)
= 4 cos (π/4) - 2 sin(π/3)
= 4(√2/2) - 2(√3/2)
= (4√2 - 2√3)/2
To find the exact value of the expression 4cos(7π/4) - 2sin(π/3), you can use the trigonometric identities and the values of cosine and sine at specific angles.
1. Start with the first term: 4cos(7π/4).
- Using the angle addition identity for cosine: cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
- Rewrite 7π/4 as the sum of two angles: 7π/4 = π + 3π/4
- Apply the angle addition identity: cos(7π/4) = cos(π)cos(3π/4) - sin(π)sin(3π/4)
- Since cos(π) = -1 and sin(π) = 0, we have: cos(7π/4) = -cos(3π/4)
2. Now evaluate the second term: -2sin(π/3).
- Sine of π/3 = √3/2 (This value can be found on a reference table or by using the unit circle.)
3. Substitute the values back into the original expression:
- 4cos(7π/4) - 2sin(π/3) = 4(-cos(3π/4)) - 2(√3/2)
- Simplify: -4cos(3π/4) - √3
4. Now evaluate the cosine of 3π/4.
- Cosine of 3π/4 = √2/2 (This value can be found on a reference table or by using the unit circle.)
5. Substitute the value back into the expression:
- -4(√2/2) - √3
- Simplify: -2√2 - √3
Thus, the exact value of 4cos(7π/4) - 2sin(π/3) is -2√2 - √3.