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kondaur [170]
2 years ago
10

If 4sintheta = -3, solve for theta given 0°>_theta>_360°

Mathematics
1 answer:
Soloha48 [4]2 years ago
6 0

Answer:

311.41 degrees

Step-by-step explanation:

If 4 sin Ф = -3 and Ф is between 0 and 360 degrees, then we conclude that Ф must be either in Quadrant III or Quadrant IV (because the sine is negative).

Let's assume we're in Quadrant IV.  Then sin Ф = opp / hyp = -3/4; that is, the opp side is negative and has length 3, and the hypo is positive 4.

According to the Pythagorean Theorem,  (-3)^2 + x^2 = 4^2, or,

x^2 = 16 - 9 = 7.

Then x is either √7 or -√7.

To find the angle Ф, use the inverse sine function:

Ф = arcsin (-3/4).  Using a calculator we get the angle -40.59 degrees, which corresponds to (360 degrees - 40.59 degrees), or 311.41 degrees.  We can check this by finding the sine of 311.41 degrees; the result is -0.75, which matches "If 4sintheta = -3."  

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Select the lengths in centimeters that would form a right triangle
Ivenika [448]

Answer:

9, 40 and 41

Step-by-step explanation:

All right triangle have lengths that follow the Pythagorean Theorem (a²+b² = c²).  Right triangles have one angle equal to 90°.  The two shorter sides form the right angle and the side opposite the right angle is called the hypotenuse.  

Using the lengths given, we can use guess and check to see what sum of two sides squared would equal a third side, or just plug them into the equation: a²+b² = c² and see what lengths fit this equation.  

I recommend starting with squares you are familiar with:

9² + 40²= 81 + 1600 = 1681

Now, take the √1681 to find the length of 'c', or the hypotenuse:

√1681  = 41

Since these three lengths fit the Pythagorean Theoreom, the would form a right triangle.

4 0
2 years ago
If D is the center of the circle below and AC measures 48, what is the measure of ABC
dimulka [17.4K]

Answer:

24

Step-by-step explanation:

How do we know that a circle must complete up to 180, then we have to:

180 - 48 = 132

Now knowing this distance we can also know the other, starting from the same concept, in addition to what the circle below is like, a semicircle refers to so we divide by 2:

(180-132) / 2 = 24

Therefore the answer is 24.

We can also do it ABC is half of ADC. So ABC = 48/2 = 24

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2 years ago
Help please 10 points
Mazyrski [523]
Im guessing it would be about 50 degrees
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2 years ago
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sammy [17]

The correct statement about the data collected by Ms. Pearson is that there is no association between a student's absences and the final average grades.

<h3>When do variables have a linear relationship?</h3>

The equation that represents a linear relationship is: a + bx

Where x represents the rate of increase. Thus, for linear equations, the functiion increases by a constant term.

Looking at the table, the average final grade does not increase by a constant term.

To learn more about linear functions, please check: brainly.com/question/26434260

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1 year ago
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What is the common ratio between successive terms in the sequence?

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of

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2 years ago
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