# Find the Other Trig Values in Quadrant II csc(theta) = square root of 2

Find the Other Trig Values in Quadrant II csc(theta) = square root of 2
Use the definition of cosecant to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.
Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.
Replace the known values in the equation.
Negate .
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.
One to any power is one.
Multiply by .
Subtract from .
Any root of is .
Multiply by .
Find the value of sine.
Use the definition of sine 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 cosine.
Use the definition of cosine 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 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 secant.
Use the definition of secant 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 six hundred twenty-six million eight hundred sixty-one thousand six hundred eighty-seven

### Interesting facts

• 626861687 has 4 divisors, whose sum is 638689320
• The reverse of 626861687 is 786168626
• Previous prime number is 53

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 50
• Digital Root 5

### Name

Name one billion eight hundred sixty-seven million one hundred thirty thousand two hundred ninety-six

### Interesting facts

• 1867130296 has 16 divisors, whose sum is 6301564776
• The reverse of 1867130296 is 6920317681
• Previous prime number is 2

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 43
• Digital Root 7

### Name

Name two billion one hundred fifteen million three hundred thirty-four thousand three hundred six

### Interesting facts

• 2115334306 has 8 divisors, whose sum is 3180995100
• The reverse of 2115334306 is 6034335112
• Previous prime number is 397

### Basic properties

• Is Prime? no
• Number parity even
• Number length 10
• Sum of Digits 28
• Digital Root 1