Find the Other Trig Values in Quadrant IV sec(theta) = square root of 2

Find the Other Trig Values in Quadrant IV sec(theta) = square root of 2
Use the definition of secant to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Find the opposite side of the unit circle triangle. Since the adjacent side and hypotenuse are known, use the Pythagorean theorem to find the remaining side.
Replace the known values in the equation.
Negate .
Opposite
Rewrite as .
Use to rewrite as .
Opposite
Apply the power rule and multiply exponents, .
Opposite
Combine and .
Opposite
Cancel the common factor of .
Cancel the common factor.
Opposite
Rewrite the expression.
Opposite
Opposite
Evaluate the exponent.
Opposite
Opposite
One to any power is one.
Opposite
Multiply by .
Opposite
Subtract from .
Opposite
Any root of is .
Opposite
Multiply by .
Opposite
Opposite
Find the value of sine.
Use the definition of sine to find the value of .
Substitute in the known values.
Simplify the value of .
Move the negative in front of the fraction.
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 .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Find the value of cosine.
Use the definition of cosine to find the value of .
Substitute in the known values.
Simplify the value of .
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 .
Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Find the value of tangent.
Use the definition of tangent to find the value of .
Substitute in the known values.
Divide by .
Find the value of cotangent.
Use the definition of cotangent to find the value of .
Substitute in the known values.
Divide by .
Find the value of cosecant.
Use the definition of cosecant to find the value of .
Substitute in the known values.
Simplify the value of .
Move the negative one from the denominator of .
Rewrite as .
This is the solution to each trig value.
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Name

Name five hundred forty-one million two hundred ninety thousand eight hundred twenty-eight

Interesting facts

• 541290828 has 64 divisors, whose sum is 1750668192
• The reverse of 541290828 is 828092145
• Previous prime number is 1993

Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 39
• Digital Root 3

Name

Name one hundred twenty-one million two hundred fifty-five thousand four hundred seventy-two

Interesting facts

• 121255472 has 128 divisors, whose sum is 711943344
• The reverse of 121255472 is 274552121
• Previous prime number is 13

Basic properties

• Is Prime? no
• Number parity even
• Number length 9
• Sum of Digits 29
• Digital Root 2

Name

Name one billion eight hundred twenty-seven million four hundred eighty-six thousand seven hundred ninety-four

Interesting facts

• 1827486794 has 16 divisors, whose sum is 3240864000
• The reverse of 1827486794 is 4976847281
• Previous prime number is 29

Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 56
• Digital Root 2