Posted by **Priya** on Tuesday, December 18, 2012 at 8:28pm.

If the given point is on the terminal arm of an angle A in stadard position. 0 degrees more than or equal too A and less than or equal too 180 degree, find sin A and cos A:

a) (6,8) b) (-5,12)

Can you tell me how you get it because I do not understand it at all please help!

- Grade 11 math -
**Reiny**, Tuesday, December 18, 2012 at 8:51pm
based on a right-angled triangle , you probably originally learned the following definitions of trig functions:

sinŲ = opposite/hypotenuse

cosŲ = adjacent/hypotenuse

tanŲ = opposite/adjacent

by now I hope you also learned them in the following terms

sinŲ = y/r

cosŲ = x/r

tanŲ = y/x

So after drawing your triangle for the terminal point (6,8)

we know x=6, y=8 and r^2 = x^2 + y^2 = 100

so r = 10

so for the angle in the first quadrant

sinŲ = 8/10 = 4/5

cosŲ = 6/10 = 3/5

tanŲ = 8/6 = 4/3

for the point (-5,12) the triangle is in the 2nd quadrant,

x = -5, y = 12, and r = 13 , (r is considered always positive)

sinŲ = 12/13

cosŲ = -5/13

tanŲ = -12/5

no matter what point you are given, plot the point and you will see which quadrant you are in.

Draw the perpendicular to the x-axis (not the y-axis) and follow the steps I outlined.

- Grade 11 math -
**Priya**, Tuesday, December 18, 2012 at 8:59pm
I don'tquite understand we never learned y and r stuff. We just started this..the chapter is called Angles of rotation. Andwhere did u get the 10 from... and um sorry for bothering you but can u help me do one because there are many..:(

Thanks I greatly appreciate you help!

- Grade 11 math -
**Reiny**, Tuesday, December 18, 2012 at 9:15pm
plot (6,8)

join to the origin (0,0)

from (6,8) draw a perpendicular to the x-axis

to get a right-angled triangle , with the line from the origin to the point (6,8) as the hypotenuse.

If you are studying trig you must have learned the Pythagorean Theorem

let the length of the hypotenuse be r

then r^2 = 6^2 + 8^2

r^2 = 36+64 = 100

r = √100 = 10

if you label the rotated angle Ų,

then

sinŲ = opposite/hypotenuse = 8/10 = 4/5

etc, see above

notice for the point (6,8), the 6 is the x value, and the 8 is the y value.

I hope that they will teach you very soon the trig definitions in terms of x, y , and r

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