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Quadrants and Angles (page 3 of 3) Sections: Introduction, Worked Examples (and Sign Chart), More Examples
The tangent is positive in QI and in QIII. The sine ratio is negative in QIII and QIV. The overlap is QIII, so α must terminate in the third quadrant. In the third quadrant, each of x and y is negative, so the numerator and denominator of the tangent ratio y/x are both negative.
Then the other ratios are: The answers for the cosecant and cotangent can be expressed in either of two ways, depending on whether your particular text book still cares whether you leave radicals in the denominator. Your calculus book probably won't care; your algebra book definitely did care; trig books vary. If you're not sure what is the protocol for your class, ask your instructor.
This is an unusual sort of exercise, but I can use what I've learned in algebra to pick it apart. First, I'll solve for "y=" to get the equation y = –(5/3)x. From what I remember of graphing, this is an decreasing line through the origin, so it passes through QII and QIV. Since they gave me the restriction that x is negative, then the angle alpha must end in QII.
The height is y = 5 and the base is x = –3, so the hypotenuse is given by:
Then the six trig ratios are: << Previous Top  1  2  3  Return to Index



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