# Find Trig Functions Using Identities sec(t)=2 , sin(t)<0

Find Trig Functions Using Identities sec(t)=2 , sin(t)<0
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The sine function is negative in the third and fourth quadrants. The secant function is positive in the first and fourth quadrants. The set of solutions for are limited to the fourth quadrant since that is the only quadrant found in both sets.
Solution is in the fourth quadrant.
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
Raise to the power of .
Opposite
One to any power is one.
Opposite
Multiply by .
Opposite
Subtract from .
Opposite
Opposite
Find the value of sine.
Use the definition of sine to find the value of .
Substitute in the known values.
Move the negative in front of the fraction.
Find the value of cosine.
Use the definition of cosine to find the value of .
Substitute in the known values.
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.
Simplify the value of .
Cancel the common factor of and .
Rewrite as .
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 cosecant.
Use the definition of cosecant 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.
This is the solution to each trig value.
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### Name

Name one billion seven hundred thirty million ninety-six thousand four hundred eighty-nine

### Interesting facts

• 1730096489 has 8 divisors, whose sum is 1902240768
• The reverse of 1730096489 is 9846900371
• Previous prime number is 127

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 47
• Digital Root 2

### Name

Name seven hundred fifty-nine million three hundred ninety-six thousand six hundred five

### Interesting facts

• 759396605 has 4 divisors, whose sum is 760652412
• The reverse of 759396605 is 506693957
• Previous prime number is 605

### Basic properties

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

### Name

Name one billion forty million five hundred fifty-nine thousand forty-five

### Interesting facts

• 1040559045 has 32 divisors, whose sum is 1164147712
• The reverse of 1040559045 is 5409550401
• Previous prime number is 61

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 10
• Sum of Digits 33
• Digital Root 6