I have absolutely no idea how to do this trig crap. I have really no chance of passing precalc at this point after completely failing the last test on logs, but I just want to understand everything as best I can so my money wasn't completely wasted. This is just way too much stuff for anyone to have to memorize.
Anyone know what the hell this question is even asking? I know csc is 1/sin (hyp/opp) but I don't understand the whole 0 ≤ θ ≤ π/2 part.
Anyone know what the hell this question is even asking? I know csc is 1/sin (hyp/opp) but I don't understand the whole 0 ≤ θ ≤ π/2 part.
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You are probably familiar with angles expressed in degrees, but in trigonometry and especially calculus, angles are more often expressed in radians. Zero degrees is by convention the direction of the positive X axis, 90 degrees the positive Y axis, 180 degrees the negative X axis, and 270 degrees the negative Y axis.
Imagine a circle with radius of one unit, located at the origin. The angle in radians is the distance along the circumference of that circle, starting at (1,0) and going counterclockwise. Since the circumference is 2πr, the distance around the entire circle is 2π. Each 90 degree angle is 1/4 of that, or π/2. So 0 ≤ θ ≤ π/2 just means that the angle is in the first quadrant (positive X, positive Y).
The cosine of an angle is simply the X value of the corresponding point on that unit circle, while the sine of the angle is the Y value. (Because the length of the hypotenuse is always one.)
The quadrant is specified because 1/sinθ = 1.4736 has two solutions, one in the first quadrant and one in the second quadrant. To calculate the answer, you use your calculator to get sin^-1(1/1.4736) = ~ 0.746 assuming you remembered to set it to radians. Otherwise, you would get 42.735 degrees.
If the problem asked for the solution in the second quadrant, you would have to subtract this from π (or from 180 degrees).
If you want to convert an angle in radians to degrees, multiply by 180/π. To convert from degrees to radians, multiply by π/180.
Imagine a circle with radius of one unit, located at the origin. The angle in radians is the distance along the circumference of that circle, starting at (1,0) and going counterclockwise. Since the circumference is 2πr, the distance around the entire circle is 2π. Each 90 degree angle is 1/4 of that, or π/2. So 0 ≤ θ ≤ π/2 just means that the angle is in the first quadrant (positive X, positive Y).
The cosine of an angle is simply the X value of the corresponding point on that unit circle, while the sine of the angle is the Y value. (Because the length of the hypotenuse is always one.)
The quadrant is specified because 1/sinθ = 1.4736 has two solutions, one in the first quadrant and one in the second quadrant. To calculate the answer, you use your calculator to get sin^-1(1/1.4736) = ~ 0.746 assuming you remembered to set it to radians. Otherwise, you would get 42.735 degrees.
If the problem asked for the solution in the second quadrant, you would have to subtract this from π (or from 180 degrees).
If you want to convert an angle in radians to degrees, multiply by 180/π. To convert from degrees to radians, multiply by π/180.