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 , we first need to convert the mixed angle of degrees and minutes into a decimal form.
Steps:
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Convert the minutes (48') into a decimal by dividing by 60:
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Add this to the degrees part:
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Now, we can find the sine of using a calculator or trigonometric function.
Using a calculator:
So, the decimal approximation of is approximately:
Let me know if you'd like further clarification or more details! Here are a few related questions for your reference:
- How do you convert between degrees, minutes, and seconds in trigonometric calculations?
- What is the effect of a negative angle on the sine function?
- How can you verify the result of trigonometric functions on a calculator?
- How would the sine of an angle in the second quadrant differ from one in the fourth quadrant?
- 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