# Trigonometry Examples

Find the Sine (3 1/2,-2 square root of 15)
To find the between the x-axis and the line between the points and , draw the triangle between the three points , , and .
Opposite :
Find the hypotenuse using Pythagorean theorem .
A mixed number is an addition of its whole and fractional parts.
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Simplify the expression.
Apply the product rule to .
Raise to the power of .
Raise to the power of .
Apply the product rule to .
Raise to the power of .
Rewrite as .
Rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Evaluate the exponent.
Multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Rewrite as .
Simplify the numerator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Simplify the denominator.
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
therefore .
Simplify .
Multiply the numerator by the reciprocal of the denominator.
Multiply .
Combine and .
Multiply by .
Combine and .
Move the negative in front of the fraction.
Approximate the result.