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Giu1iano
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Homework Statement
P(-5,-2) is a terminal point of angle theta in standard position. State the exact values of all the trigonometric rations for theta.
Homework Equations
x^2+y^2=r^2
csc=1/sin
sec=1/cos
cot=1/tan
Giu1iano said:Homework Statement
P(-5,-2) is a terminal point of angle theta in standard position. State the exact values of all the trigonometric rations for theta.
Homework Equations
x^2+y^2=r^2
csc=1/sin
sec=1/cos
cot=1/tan
The Attempt at a Solution
View attachment 113737
Pos in quadrant 1 neg in quadrant 3LCKurtz said:In what quadrants are tan and cot positive vs negative?
Explain. I learn "CAST" to help remember that but first you explainLCKurtz said:Wrong. Look in your text.
The six trigonometric ratios for theta are sine, cosine, tangent, cotangent, secant, and cosecant.
To find the exact values of the trigonometric ratios for theta, you can use a calculator or reference a trigonometric table. Alternatively, you can use the Pythagorean identity and the values of the adjacent, opposite, and hypotenuse sides of a right triangle to calculate the ratios.
Yes, the values of the trigonometric ratios for theta can be negative, depending on the quadrant in which theta lies. For example, in quadrant II, only the sine and cosecant ratios are positive, while in quadrant III, only the tangent and cotangent ratios are positive.
Yes, there are special values for certain angles of theta. For example, for theta = 0, the values of cosine and secant are both 1, and the values of sine and tangent are both 0. For theta = 30 degrees, the values of sine and cosecant are both 1/2, and the values of cosine and secant are both √3/2.
The trigonometric ratios for theta are related to each other through various identities and equations. For example, the Pythagorean identity states that sine squared plus cosine squared equals 1, and the reciprocal identities state that sine is equal to 1 over cosecant and cosine is equal to 1 over secant. These relationships can be used to find the value of one trigonometric ratio if the values of the others are known.