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This algebra 2 math tutorial from NutshellMath offers targeted homework help on evaluating trigonometric functions for general angles. The instructions is focused on problems 2, 3, 15, 17, 19, 22, and 45-52 on pages 788 and 789 of the Algebra 2: Applications, Equations, Graphs text from McDougal Littell. Homework problems like these will involve evaluating the six major trigonometric functions for a given angle.
This tutorial offers several steps to evaluating trigonometric functions for a given angle. First, it is necessary to sketch the angle and find a reference angle. This is best done on a unit circle on the coordinate plane. Any angle can be sketched as starting from the positive x-axis as a rotation about the origin. Once sketched, the angle can be compared to an acute angle from the positive or negative x-axis in either direction. Using this reference angle, it is possible to draw a right triangle, using the radius of the unit circle as the hypotenuse.
The next step is to determine the sign of the trigonometric functions in that quadrant and evaluate. It is easy to calculate the sign of any trigonometric functions knowing that sine will be positive for quadrants above the x-axis and negative below, and that cosine will be positive for quadrants to the right of the y-axis and negative to the left. To evaluate the trig function, it is best to first evaluate cosine and sine, and use those to calculate the other functions. On a unit circle, cosine will simply be the length of the horizontal leg of the reference triangle, and sine will be the length of the vertical leg, paying attention to sign for each. Using these values, it is possible to calculate the other four trigonometric functions. When finding the values for trig functions, it is also important to rationalize denominators by moving radicals to the numerator.
The examples in this tutorial will reinforce these steps for evaluating trigonometric functions of general angles. This method can be used to solve homework problems such as those in the text, which ask for exact values of trigonometric functions given an angle measurement.
This algebra 2 math tutorial from NutshellMath offers targeted homework help on evaluating trigonometric functions for general angles. The instructions is focused on problems 2, 3, 15, 17, 19, 22, and 45-52 on pages 788 and 789 of the Algebra 2: Applications, Equations, Graphs text from McDougal Littell. Homework problems like these will involve evaluating the six major trigonometric functions for a given angle.
This tutorial offers several steps to evaluating trigonometric functions for a given angle. First, it is necessary to sketch the angle and find a reference angle. This is best done on a unit circle on the coordinate plane. Any angle can be sketched as starting from the positive x-axis as a rotation about the origin. Once sketched, the angle can be compared to an acute angle from the positive or negative x-axis in either direction. Using this reference angle, it is possible to draw a right triangle, using the radius of the unit circle as the hypotenuse.
The next step is to determine the sign of the trigonometric functions in that quadrant and evaluate. It is easy to calculate the sign of any trigonometric functions knowing that sine will be positive for quadrants above the x-axis and negative below, and that cosine will be positive for quadrants to the right of the y-axis and negative to the left. To evaluate the trig function, it is best to first evaluate cosine and sine, and use those to calculate the other functions. On a unit circle, cosine will simply be the length of the horizontal leg of the reference triangle, and sine will be the length of the vertical leg, paying attention to sign for each. Using these values, it is possible to calculate the other four trigonometric functions. When finding the values for trig functions, it is also important to rationalize denominators by moving radicals to the numerator.
The examples in this tutorial will reinforce these steps for evaluating trigonometric functions of general angles. This method can be used to solve homework problems such as those in the text, which ask for exact values of trigonometric functions given an angle measurement.