How do you find the exact value of:
4sin 60degrees - 3tan 135degrees
You should know the trig ratios of the 30-60-90 and the 45-45-90 right-angled triangles
sin 60° = √3/2
so 4sin60° = 4(√3/2) = 2√3
tan 135° = -tan 45° = -1
now put it all together to get
2√3 + 3
To find the exact value of the expression 4sin 60° - 3tan 135°, we can break it down step by step.
Step 1: Evaluate sin 60°
The sine of 60° is equal to √3/2. This can be found using the special triangles or by using the unit circle.
Step 2: Evaluate tan 135°
The tangent of 135° is equal to -1. This can be found by recognizing that 135° is in the second quadrant, where the tangent is negative. Alternatively, you can use the unit circle.
Step 3: Substitute the values into the expression.
Now that we know sin 60° = √3/2 and tan 135° = -1, we can substitute these values into the expression:
4sin 60° - 3tan 135° = 4(√3/2) - 3(-1)
Step 4: Simplify the expression.
By applying the distributive property, we can simplify as follows:
4(√3/2) - 3(-1) = 2√3 - (-3) = 2√3 + 3
Therefore, the exact value of the expression 4sin 60° - 3tan 135° is 2√3 + 3.