# Trigonometry Examples

Find the Sine (-1/( square root of 10),3/( square root of 10))
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 .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
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.
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Simplify the expression.
Raise to the power of .
Multiply by .
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.
Raise to the power of .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
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.
Use the power rule to distribute the exponent.
Apply the product rule to .
Apply the product rule to .
Simplify the numerator.
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.
Reduce the expression by cancelling the common factors.
Raise to the power of .
Multiply by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine the numerators over the common denominator.
Divide by .
Any root of is .
therefore .
Simplify .
Divide by .
Multiply by .
Combine and simplify the denominator.
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.