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Ket [755]
3 years ago
6

Suppose theta is an angle in the standard position whose terminal side is in Quadrant II and tan0= -sqrt3 Find the exact values

of the remaining five trigonometric functions of theta
Mathematics
1 answer:
diamong [38]3 years ago
3 0

The exact values of the remaining <u>five</u> trigonometric functions of theta are

  • sinθ = √3/2
  • cosecθ = 2/√3
  • cosθ = -1/2
  • secθ = -2
  • cotθ = -1/√3

Since tanθ = -√3.

The remaining <u>five</u> trigonometric functions of theta are sinθ, cosecθ, cosθ, secθ and cotθ.

The next trigonometric function of θ is cotθ.

cotθ = 1/tanθ

= 1/-√3

= -1/√3.

Also, tan²θ + 1 = sec²θ

Substituting tanθ = -√3 into the equation, we have

(-√3)² + 1 = sec²θ

3 + 1 = sec²θ

sec²θ = 4

secθ = ±√4

secθ = ±2

Since θ is in the quadrant II,

secθ = -2

Also, cosθ = 1/secθ

= 1/-2

= -1/2

Also, cot²θ + 1 = cosec²θ

Substituting cotθ = -1/√3 into the equation, we have

(-1/√3)² + 1 = cosec²θ

1/3 + 1 = cosec²θ

cosec²θ = 4/3

cosecθ = ±√(4/3)

cosecθ = ±2/√3

Since θ is in the quadrant II,

cosecθ = +2/√3

Also, sinθ = 1/cosecθ

= 1/2/√3

= √3/2

So, the exact values of the remaining <u>five</u> trigonometric functions of theta are

  • sinθ = √3/2
  • cosecθ = 2/√3
  • cosθ = -1/2
  • secθ = -2
  • cotθ = -1/√3.

Learn more about trigonometric functions here:

brainly.com/question/4515552

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Enter your answer and show all the steps that you use to solve this problem in the space provided.
rodikova [14]

Answer:

\boxed{f(x) - g(x) = 2x(2x^{2} + x + 1)}

Step-by-step explanation:

f(x) = 9x³ + 2x² - 5x + 4; g(x)=5x³ -7x + 4

Step 1. Calculate the difference between the functions

(a) Write the two functions, one above the other, in decreasing order of exponents.

ƒ(x) = 9x³ + 2x² - 5x + 4

g(x) = 5x³           - 7x + 4

(b) Create a subtraction problem using the two functions

        ƒ(x) =    9x³ + 2x² - 5x + 4

      -g(x) =  <u>-(5x³           - 7x + 4) </u>

ƒ(x) -g(x)=

(c). Subtract terms with the same exponent of x

        ƒ(x)   =    9x³ + 2x² - 5x + 4

      -g(x)  =   <u>-(5x³          -  7x + 4) </u>

ƒ(x) -g(x) =      4x³ + 2x² + 2x

Step 2. Factor the expression

y = 4x³ + 2x² + 2x

Factor 2x from each term

y = 2x(2x² + x + 1)

\boxed{f(x) - g(x) = 2x(2x^{2} + x + 1)}

5 0
3 years ago
Two fifths of one less than a number is less than three fifths of one more than that number .what numbers are in the solution se
Lelechka [254]

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To find the solution, we can use the distributive property to simplify.

2/5x - 2/5 < 3/5 + 3/5x

Multiply all terms by 5.

2x - 2 < 3 + 3x

Subtract 2x from both sides.

-2 < 3 + x

Subtract 3 from both sides.

-5 < x

<h3><u>The value of x is greater than the value of -5.</u></h3>
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8_murik_8 [283]

Answer:

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Step-by-step explanation:

The first choice

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Answer:

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