Solving for Angle 'a' in Quadrant 2: Math Homework

In summary, to find the measure of angle 'a' in the second quadrant given the equation (csc a) = (sec 0.75), you can use the reciprocal and quotient identities. By finding that cos(0.75) = 0.7317 and sin(a) = 0.7317, you can use a calculator to find that a = 2.3208, which can be rounded to 2.32 to two decimal places.
  • #1
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Homework Statement



Given that (csc a) = (sec0.75) and that 'a' lies in the second quadrant, determine the measure of angle 'a', to two decimal places.

Homework Equations



reciprocal and quotient identities.

The Attempt at a Solution



I only got as far as:

1/sin(a) = 1/cos(0.75)

The answer in the back of the book is 2.32

Can anyone guide me towards the light? thanks in advance!
 
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  • #2


Well, it is not difficult to find that cos(.75)= .7317 using a calculator and , again using a calculator, that sin(a)= .7317 for a= .8208. Of course, that is the "principal root", less than [itex]\pi/2[/itex]. Since a is in the second quadrant, a= [itex]\pi[/itex]- .8208= 2.3208
 

Related to Solving for Angle 'a' in Quadrant 2: Math Homework

What is quadrant 2 in math?

Quadrant 2 in math refers to the second quadrant of a coordinate plane, which is located in the upper left quadrant. In this quadrant, both the x and y coordinates are negative.

Why is it important to solve for angle 'a' in quadrant 2?

Solving for angle 'a' in quadrant 2 is important because it helps us determine the exact position of a point on a coordinate plane. This is crucial in various mathematical applications, such as graphing and solving equations.

How do I solve for angle 'a' in quadrant 2?

To solve for angle 'a' in quadrant 2, you can use the trigonometric functions sine, cosine, and tangent. First, identify the given side lengths or angles and then use the appropriate function to find the missing angle.

What are the common mistakes when solving for angle 'a' in quadrant 2?

One common mistake when solving for angle 'a' in quadrant 2 is forgetting to change the sign of the angle or side length when using trigonometric functions. For example, if the angle is given as -30 degrees, it should be changed to +30 degrees when using the trigonometric functions.

Can there be more than one solution when solving for angle 'a' in quadrant 2?

Yes, there can be more than one solution when solving for angle 'a' in quadrant 2. This is because the reference angle, which is the angle between the terminal side and the x-axis, can be used to find multiple angles in the quadrant.

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