without using mathematical table evaluate sin30-sin60/tan60
You must memorize the ratio of sides of the standard
30-60-90 ° triangle to be 1 : √3 : 2 respectively
then sin30° = 1/2
sin 60° = √3/2
tan 60° = √3/1 =√3
assuming you meant:
(sin30-sin60)/tan60
= (1/2 - √3/2)/√3
= (1/2 - √3/2)/√3* √3/√3
= (√3 - 3)/6
sin30 - sin60/tan60 = sin30 - cos60 = sin30 - sin30 = 0
To evaluate the expression sin30 - sin60/tan60 without using a mathematical table, we can use the trigonometric properties and some basic calculations. Here's the step-by-step solution:
Step 1: Simplify the expression sin30 - sin60/tan60
Since sin30 = 1/2 and tan60 = √3, we can substitute these values into the expression:
1/2 - sin60/√3
Step 2: Simplify sin60
Using the trigonometric identity sin60 = √3/2, we can substitute this value into the expression:
1/2 - (√3/2)/√3
Step 3: Simplify the denominator
The denominator √3 can be simplified:
1/2 - (√3/2)/(√3/√3)
1/2 - (√3/2)/1
Step 4: Multiply the numerator and denominator by the conjugate of the fraction (√3/2)
The conjugate of (√3/2) is (√3/2):
(1/2 - (√3/2)/1) * (√3/2)/(√3/2)
(1√3 - (√3/2)²)/2
Step 5: Simplify the expression in the numerator
(1/2 - (3/2))/2
(-2/2)/2
-1/2
Therefore, the simplified expression for sin30 - sin60/tan60 is -1/2.
To evaluate the expression sin30 - sin60/tan60 without using a mathematical table, we can rely on some basic trigonometric identities and the knowledge of special angles.
1. Start by converting the angles to their corresponding values in radians. Recall that sin and tan functions typically work with radians. To convert degrees to radians, multiply the degree value by π/180.
sin(30°) = sin(30 * π/180) = sin(π/6) = 0.5
sin(60°) = sin(60 * π/180) = sin(π/3) = (√3)/2
tan(60°) = tan(60 * π/180) = tan(π/3) = (√3)
2. Now, substitute these values back into the expression.
sin30 - sin60/tan60 becomes 0.5 - (√3)/2 / (√3)
3. Simplify the expression by rationalizing the denominator.
Multiply the numerator and denominator by (√3).
(0.5 * √3 - 1) / (√3 * √3)
= (0.5 * √3 - 1) / √(3 * 3)
= (0.5 * √3 - 1) / √9
= (0.5√3 - 1) / 3
So, the simplified expression without using a mathematical table is (0.5√3 - 1) / 3.