i suck at trig, someone help..?

Question

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Answer 1

Hi,

If sec A = 13/12, then its reciprocal, cos A = 12/13.

Since cos A = adjacent/hypotenuse, then 12 = adjacent side and 13 = hypotenuse.

Using the Pythagorean Theorem, we can solve for the opposite side.
Since a^2 + b^2 = c^2, then 12^2 + b^2 = 13^2.
144 + b^2 = 169
b^2 = 25
b = 5
The opposite side has a length of 5.

So sin A = opposite/hypotenuse so sin A = 5/13. Its reciprocal, csc A = 13/5.

I hope that helps!! :-)

Answer 2

All trig problems can be worked out on the "unit circle" -- a circle drawn on the cartisian grid with the center at the origin. The radius of the circle will be the hypotenous of your triangle. Sin is the ratio of the y-coordinate over the length of the radius. Cos is the ratio of the x-coordinate over the length of the hypotenous. Tan is the y-coordinate divided by the x-coordinate. http://mathworld.wolfram.com/Cosine.html
Sec = 1/Cos, Csc = 1/Sin. In your question, SEC A = 13 / 12 is the same as trying to solve COS A = 12 / 13. The radius (hypotenous) is 13. The X-coordinate is 12. SQRT(13^2-12^2) will give you the Y-coordinate of the point so you can draw the triangle on the unit circle. On your calculator, A = ARCCOS(12/13), which depending on the settings will give you an angle in degrees/minutes/seconds, or radians where 2PI() radians will let you travel all the way around the unit circle starting from the positive x-axis. Once you draw the triangle you will be able to see the angle represented by the CSC of A -- the inverse of the SIN A.

Starting from (x=1,y=0) on the circle, moving along the circumferance to (x=0,y=1) you will note that the x gets smaller and the y gets bigger (i.e., COS gets smaller and SIN gets bigger). SIN is the y-coordinate, COS is the x-coordinate. SIN and COS must always be some value between 0 and 1. TAN must be 1 on the unit circle; radius (hypotenuous) will always be 1 away from the origin. Because SEC and CSC are inverse functions, those ratios will always be bigger than one.

Answer 3

Well, secant of an angle is its hypotenuse over its adjacent angle, and co secant of an angle is its hypotenuse over its opposite angle. Given sec A is 13/12 and angle C is 90 degrees, it has to be a 5-12-13 right triangle. So csc A = 13/5

Answer 4

sec A = 13/12
1 / cos A = 13/12
cos A = 12 / 13 (A in 1st quadrant)
sin A = 5 / 13 (5 , 12 ,13 is a standard 90° triangle)
1 / sin A = 13 / 5
cosec A = 13 / 5

Answer 5

This looks like a 5, 12, 13 right triangle. secant means hyp/adj
so 12 is the adjacent side. Cosecant is the reciprocal of sin so it is hyp/opp. The opposite side would be 5 and the hypotenuse is definitely the longest side, 13.
13/5 is cscA

Answer 6

Pythagorean theorem

sec = r/x

csc = r/y

r = 13

x = 12

x^2 + y^2 = r^2

144 + y^2 = 169

y = 5

csc A = r/y = 13/5

Answer 7

i think of there's a typo. commencing from the purple underlined ingredient, (sin^2 A)(a million - sin^2 B) - (a million - sin^2 A)(sin^2 B) = sin^2 A - sin^2 A sin^2 B - sin^2 B + sin^2 A sin^2 B = sin^2 A - sin^2 B the point of the evidence replaced into to coach that: sin(A - B) * sin(A + B) = sin^2 A - sin^2 B :D