evaluate (sin 30°-sin60°)/tan60°
recall that
sin30° = 1/2
sin60° = cos30° = √3/2
(sin^2+cos^2 = 1)
tan60° = cot30° = cos30°/sin30° = √3
recall that co-f(x) = f(90°-x)
That is, the co-function is the function of the complement!
Well, let's break down the expression step by step, shall we?
First, sin 30° is equal to 0.5, and sin 60° is equal to √3/2. So, the numerator becomes (0.5 - √3/2).
Next, let's tackle the denominator. tan 60° is equal to √3. So, the denominator is simply √3.
Now, let's simplify the expression:
(0.5 - √3/2) / √3
Hmm, not the most straightforward expression, is it? It could use a little makeover. How about we get rid of that pesky square root in the denominator by multiplying the expression by √3/√3?
[(0.5 - √3/2) / √3] * (√3/√3)
Now, we can distribute the √3 and simplify:
[0.5√3 - (√3/2)√3] / 3
Finally, after a bit more simplification, we have:
[(0.5√3 - √3 * √3/2)] / 3
And, since √3 * √3 equals 3, we can further simplify:
[(0.5√3 - 3/2)] / 3
Voila! We've reached our final answer: (0.5√3 - 3/2) / 3
I hope this mathematical journey wasn't too square for you!
To evaluate the expression `(sin 30° - sin 60°) / tan 60°`, follow these steps:
Step 1: Use a calculator or trigonometric tables to find the numerical values of sin 30°, sin 60°, and tan 60°.
- sin 30° = 0.5
- sin 60° = (√3)/2
- tan 60° = (√3)
Step 2: Substitute these values into the expression:
- (0.5 - (√3)/2) / (√3)
Step 3: Simplify the expression further:
- Multiply the numerator and denominator by (√3) to get rid of the denominator:
(0.5 - (√3)/2) * (√3) / (√3) * (√3)
= (0.5√3 - 3/2) / (√3 * (√3))
= (0.5√3 - 1.5√3) / 3
= (-1√3) / 3
= -√3 / 3
Therefore, the simplified expression of `(sin 30° - sin 60°) / tan 60°` is `-√3 / 3`.
To evaluate the expression (sin 30° - sin 60°) / tan 60°, we can follow the steps below:
Step 1: Calculate the values of sin 30°, sin 60°, and tan 60°.
Step 2: Substitute the values into the expression.
Step 3: Perform the necessary calculations.
Let's start with step 1:
1. Values of sin 30°, sin 60°, and tan 60°:
- sin 30° = 1/2
- sin 60° = √3/2
- tan 60° = √3
Now we can move to step 2:
2. Substitute the values into the expression:
(sin 30° - sin 60°) / tan 60° = (1/2 - √3/2) / √3
Finally, in step 3, we simplify the expression:
3. Simplify the expression:
To simplify the expression, we can multiply both the numerator and denominator by √3 to eliminate the radical in the denominator:
((1/2 - √3/2) / √3) * (√3 / √3)
= (1/2√3 - √3/2√3) / (3/√3)
= (1/2√3 - √3/2√3) / (3/√3)
= (1 - 2√3) / (2√3) / (3/√3)
= (1 - 2√3) / (2√3) * (√3/3)
= (√3 - 2√3√3) / (6√3)
= (√3 - 2√3√3) / (6√3)
= (√3 - 2√3 * √3) / (6√3)
= (√3 - 2√9) / (6√3)
= (√3 - 2√(3^2)) / (6√3)
= (√3 - 6) / (6√3)
So, the simplified expression is (√3 - 6) / (6√3).