Trig Funct of Gen Angles - IG TR RY ET M NO O T NC FU NS IO...

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TRIGONOMETRY FUNCTIONS OF GENERAL ANGLES
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Our method of using right triangles only works for acute angles. Now we will see how we can find the trig function values of any angle. To do this we'll place angles on a rectangular coordinate system with the initial side on the positive x -axis. θ HINT: Since it is 360° all the way around a circle, half way around (a straight line) is 180° If θ is 135°, we can find the angle formed by the negative x -axis and the terminal side of the angle. This is an acute angle and is called the reference angle . reference angle What is the measure of this reference angle? =135° 180°- 135° = 45° Let's make a right triangle by drawing a line perpendicular to the x -axis joining the terminal side of the angle and the x -axis.
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Let's label the sides of the triangle according to a 45-45-90 triangle. (The sides might be multiples of these lengths but looking as a ratio that won't matter so will work) 45° θ =135° The values of the trig functions of angles and their reference angles are the same except possibly they may differ by a negative sign. Putting the negative on the 1 will take care of this problem. -1 1 2 2 1 1 - - Now we are ready to find the 6 trig functions of 135° This is a Quadrant II angle. When you label the sides if you include any signs on them thinking of x & y in that quadrant, it will keep the signs straight on the trig functions. x values are negative in quadrant II so put a negative on the 1
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-1 45° θ =135° 1 2 1 2 sin135 2 2 o h ° = = = Notice the -1 instead of 1 since the terminal side of the angle is in quadrant II where x values are negative.
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