Pure Math 30 help (trig)?

Question

Hi, how do I solve these types of questions?
Find the exact value of:
sin (5(pi))/3
tan (7(pi))/6
...etc?
I thought it was to find the degree that corresponded with that, but I suppose not..
The answers in the book showed -√3/2 (for the first)
and √3/3 for the second..
how do i get these answers?
Help would be appreciated, I've got my final exam on Monday =/

Answer 1

The trigonometric functions take an angle (in degrees or radians, doesn't matter as long as you set your calculator to the correct mode) and give a range which is a ratio of sides in a right triangle.



For instance, let us try sin(5pi/3). 5pi/3 resides in quadrant 4 and has a reference angle of pi/3. (or angle 300 degrees is in quadrant 4 and had a reference angle of 60 degrees if you are more comfortable with degrees.) The range of sin is negative in quadrant 4 (because sine is y/r and y is negative in Q IV while r is a distance, therefore always positive). Now take the sine of pi/3 (or 60 degrees), but be sure to make it negative. This particular one is found by constructing a 30-60-90 triangle, in which the side opposite of 60 (y value, if constructed in Q I) is root 3 and the hypotenuse is 2 (r value). So sin(5pi/3) ends up being -root3 / 2.







I hope that clarifies things. If you need more help with studying for the final, feel free to message me.

Answer 2

u have 2 kno your reference angles and your trig function quadrant signs-- all trig functions are positive in the first quadrant (0 to pi/2)

sin and csc, only are positive in the second quadrant (pi/2 to pi)

tan and cot, only are positive in the third quadrant (pi to 3pi/2)

cos and sec, only are positive in the fourth quadrant (3pi/2 to 2pi)



coterminal angles are essentially the same--the only difference is how many times and in which direction they revolve around the axes.

hence, u can always add or subtract 2pi to or from an angle and treat it the same as u would the original angle--then use the aforementioned sign rules according to determine the answer's (value's) sign and write that down

once u get the coterminal angle, you need to use a reference angle

to move an angle from the second quadrant to the first quadrant, subtract pi-the angle

third-->first subtract angle-pi (first to third angle plus pi)

fourth-->first 2pi-angle

now u need to memorize the values for the common first-quadrant terminating trig functions sin (pi/6) = 1/2; sin (pi/4) = (sqrt (2))/2; sin (pi/3) = (sqrt(3))/2 cos(pi/6)= (sqrt(3))/2 cos (pi/4) = (sqrt(2))/2; cos (pi/3) = 1/2 for ALL values regardless of the angle tan = sin/cos cot=cos/sin csc=1/sin sec=1/cos



the sign and the value u got are the answer

Answer 3

You are supposed to figure out what quadrant the angle is in, therefore whether the value is positive or negative. Then, the reference angle (what angle it makes with the x-axis)

5pi/3 is in quadrant 4, so it is negative.

It make an angle of pi/3 (60º) with the x axis.

-sin pi/3 =-sqrt3/2

7pi/6 is in quadrant II, tan is positive, angle is pi/6

tan pi/6 =sqrt3/3

Answer 4

u have 2 kno your reference angles and your trig place quadrant alerts-- all trig features are constructive interior the 1st quadrant (0 to pi/2) sin and csc, ultimate are constructive interior the 2d quadrant (pi/2 to pi) tan and cot, ultimate are constructive interior the third quadrant (pi to 3pi/2) cos and sec, ultimate are constructive interior the fourth quadrant (3pi/2 to 2pi) coterminal angles are extraordinarily lots a similar--the single replace is how each so often and the place direction they revolve around the axes. as a result, u can continuously upload or subtract 2pi to or from an attitude and handle it comparable to u might desire to the familiar attitude--then use the aforementioned sign regulations in keeping with inspect the respond's (importance's) sign and write that down as quickly as u get the coterminal attitude, you are able to desire to apply a reference attitude to delivery an attitude from the 2d quadrant to the standard quadrant, subtract pi-the attitude third-->first subtract attitude-pi (first to third attitude plus pi) fourth-->first 2pi-attitude now u might desire to memorize the values for the organic first-quadrant terminating trig features sin (pi/6) = one million/2; sin (pi/4) = (sqrt (2))/2; sin (pi/3) = (sqrt(3))/2 cos(pi/6)= (sqrt(3))/2 cos (pi/4) = (sqrt(2))/2; cos (pi/3) = one million/2 for ALL values regardless of the attitude tan = sin/cos cot=cos/sin csc=one million/sin sec=one million/cos the sign and the importance u offered are the respond

Answer 5

you only need to know the standard reference angles and how the functions are related to the unit circle



sin (5π/3) = - sin (2π/3) and tan (7π/6) = tan (π/6)



for these two you could also use sin[a - b ] =...and the period of the tangent function is ______