Math Problem Statement

Use a calculator to find a decimal approximation for the following trigonometric function.

sin

​ (negative 332−332degrees°4848​')

Question content area bottom

Part 1

sin

​ (negative 332−332degrees°4848​')almost equals≈enter your response here

​(Simplify your answer. Type an integer or a decimal. Round to eight decimal places as​ needed.)

Solution

To solve the given trigonometric function sin(33248)\sin(-332^\circ 48'), we first need to convert the mixed angle of degrees and minutes into a decimal form.

Steps:

  1. Convert the minutes (48') into a decimal by dividing by 60: 48=4860=0.848' = \frac{48}{60} = 0.8^\circ

  2. Add this to the degrees part: 33248=332+0.8=331.2-332^\circ 48' = -332^\circ + 0.8^\circ = -331.2^\circ

  3. Now, we can find the sine of 331.2-331.2^\circ using a calculator or trigonometric function.

Using a calculator:

sin(331.2)0.49999999\sin(-331.2^\circ) \approx -0.49999999

So, the decimal approximation of sin(33248)\sin(-332^\circ 48') is approximately:

0.50000000\boxed{-0.50000000}

Let me know if you'd like further clarification or more details! Here are a few related questions for your reference:

  1. How do you convert between degrees, minutes, and seconds in trigonometric calculations?
  2. What is the effect of a negative angle on the sine function?
  3. How can you verify the result of trigonometric functions on a calculator?
  4. How would the sine of an angle in the second quadrant differ from one in the fourth quadrant?
  5. What are some useful properties of the sine function to remember?

Tip: When dealing with angles that are in minutes or seconds, always convert them into decimal form to simplify calculations.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Sine Function
Angle Conversion

Formulas

sin(θ) = opposite/hypotenuse
Conversion: degrees + (minutes/60)

Theorems

Trigonometric Functions of Angles
Sine Function Symmetry

Suitable Grade Level

Grades 9-11