Determine B e(-360;360)
Cos(B+80)=sin(-300)cos45÷cos405
preliminary:
sin(-300)
= -sin(300) = -sin(-60) = sin60 = √3/2
cos 45 = √2/2
cos405 = cos45 = √2/2
Cos(B+80)=sin(-300)cos45÷cos405
= √3/2 * √2/2 / (√2/2) = √3/2
then
B + 80° = 30° , B + 80° = 330°, B + 80° = -330°, B+80° = -30°
B = ± 30°, ± 330°
Care to revise your final line?
Arggghhh,
forgot to subtract 80° from each of these.
so
B = ± 30°- 80°, ± 330° - 80°
= -50°, -110°, 250°, 310°
thanks oobleck
To solve this equation, we need to find the value of B that satisfies the equation:
Cos(B+80) = sin(-300)cos45 ÷ cos405
Let's break down the steps to solve this equation:
Step 1: Evaluate the given trigonometric values
- sin(-300) = sin(-60°) = -√3/2
- cos45 = √2/2
- cos405 = cos(360+45) = cos45 = √2/2
Step 2: Replace the trigonometric values in the equation
Cos(B+80) = sin(-300)cos45 ÷ cos405
Cos(B+80) = (-√3/2)*(√2/2) ÷ (√2/2)
Step 3: Simplify the equation by dividing
Cos(B+80) = (-√3/2)*(√2/2) * (2/√2)
Cos(B+80) = -(√3)
Step 4: Solve for B
Now, we need to find the angle whose cosine is -(√3). By using the unit circle or a calculator, this corresponds to an angle of 150 degrees or 5π/6 radians.
Step 5: Subtract 80 from B
B + 80 = 150
B = 150 - 80
B = 70 degrees or 7π/18 radians
Therefore, B can have two possible values: 70 degrees or 7π/18 radians.