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Tan Theta = -8/15, Pi/2<Theta<pi

 

sorry, i dont know how to put the symbols for Pi and Theta in :P

Robey1Kanobi  Jan 13, 2015

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 #2
avatar+91479 
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Tan Theta = -8/15, Pi/2<Theta<pi

 

First this is the second quad so 

sin and cosec are positive and the rest will be negative.

Now you don't need to worry about again until the end.

Finsd the length of the hypotenuse using pythagoras's theorum

then read the ratios straight of the triangle and assign the appropriate signs.    

Melody  Jan 14, 2015
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 #1
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Since we have a second quadrant angle, we have that a = 8   and b = -15    so h = √[(-8)^2 + (15)^2 ]  = √(64 + 225)  = √289) = 17

Here is a review of the 6 basic trig functions.....it should help....

Sine, cosine and tangent

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. (The word comes from the Latin sinus for gulf or bay,[1] since, given a unit circle, it is the side of the triangle on which the angle opens.) In our case

\sin A = \frac {\textrm{opposite}} {\textrm{hypotenuse}} = \frac {a} {h}.

This ratio does not depend on the size of the particular right triangle chosen, as long as it contains the angle A, since all such triangles are similar.

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse: so called because it is the sine of the complementary or co-angle.[2] In our case

\cos A = \frac {\textrm{adjacent}} {\textrm{hypotenuse}} = \frac {b} {h}.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side: so called because it can be represented as a line segment tangent to the circle, that is the line that touches the circle, from Latin linea tangens or touching line (cf. tangere, to touch).[3] In our case

\tan A = \frac {\textrm{opposite}} {\textrm{adjacent}} = \frac {a} {b}.

The acronyms "SOHCAHTOA" ("Soak-a-toe", "Sock-a-toa", "So-kah-toa") and "OHSAHCOAT" are commonly used mnemonics for these ratios.

Reciprocal functions

The remaining three functions are best defined using the above three functions.

The cosecant csc(A), or cosec(A), is the reciprocal of sin(A); i.e. the ratio of the length of the hypotenuse to the length of the opposite side:

\csc A = \frac {1}{\sin A} = \frac {\textrm{hypotenuse}} {\textrm{opposite}} = \frac {h} {a}.

The secant sec(A) is the reciprocal of cos(A); i.e. the ratio of the length of the hypotenuse to the length of the adjacent side:

\sec A = \frac {1}{\cos A} = \frac {\textrm{hypotenuse}} {\textrm{adjacent}} = \frac {h} {b}.

It is so called because it represents the line that cuts the circle (from Latin: secare, to cut).[4]

The cotangent cot(A) is the reciprocal of tan(A); i.e. the ratio of the length of the adjacent side to the length of the opposite side:

\cot A = \frac {1}{\tan A} = \frac {\textrm{adjacent}} {\textrm{opposite}} = \frac {b} {a}.

 

CPhill  Jan 13, 2015
 #2
avatar+91479 
+10
Best Answer

Tan Theta = -8/15, Pi/2<Theta<pi

 

First this is the second quad so 

sin and cosec are positive and the rest will be negative.

Now you don't need to worry about again until the end.

Finsd the length of the hypotenuse using pythagoras's theorum

then read the ratios straight of the triangle and assign the appropriate signs.    

Melody  Jan 14, 2015

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