Question

if they give you tan (theta) = sqr(3) how do you determind degree (theta) radian(theta) sin(theta) cos(theta) csc(theta) sec(theta) and Cot(theta). Please help

Answer 1

= opposite/adjacent sides,

the use hypotenuse = sqrt sum of sides squared

Answer 2

\[\tan \theta=\sqrt{3}\]
To get the other trigonometric ratios , you can use identities or you can draw a triangle with its perpendicular as sqrt(3) and base as 1 so as to make tan(theta)=sqrt(3). I am showing you using the triangle method which is easy to understand. You know the perpendicular and the base, so you can find the hypotenuse using Pythagoras' theorem which is (hyp)^2=(perpendicular)^2+(base)^2. Then you just use normal definitions of sin(theta),cos(theta) and so on to find the required ratios. To find degree(theta) you can eyeball from the given fact that 60 deg is the required angle , assuming that theta here lies in the prinicipal range of values that tan(theta) can take and to convert into radian, remember that 180 deg= pi radian , then you can use the normal unitary method to find out what 60 deg would be in terms of radians.

Answer 3

I'm still confused has to how you would put that into a triangle. Would you put it onto the hypotenuse leg?

Answer 4

Do you know what tan(theta) is?

Answer 5

I am asking that in terms of sides of a triangle.

Answer 6

its opposite/ adjacent right

Answer 7

Correct. Now length of opposite should be equal to sqrt(3) and and that of adjacent should be 1 to make tan(theta)=sqrt(3), where theta is an arbitrary angle in a right-angled triangle ,got it?

Answer 8

I think I have it so opposite is srq 3 and adjacent is 1 because of the equation. so to find sin you would do 1^2 +sqr3^=c^2?

Answer 9

To find sin, you have to find hypotenuse first using what you used above, where c is the hypotenuse.Don't forget the exponent 2 above sqrt(3). Then you use sin(theta)=opposite/hypotenuse. You can find cosec(theta) by inverting it. Similarly, you can find cos(theta)=adjacent/hypotenuse and invert it to get sec and for cot(theta) you invert tan(theta) value.

Answer 10

are the calculators still supposed to be in radiant or no

Answer 11

is 2 the hypotenuse

Answer 12

Yes, now just plug in the values to get the respective trigonometric ratios.

Answer 13

sin sqr3/2 ,cos=1/2, sec is 2/1, cot= 1/sqr3, csc=2/sqr3

Answer 14

Yes, you got the ratios correct. Well done.

Answer 15

thank you

Answer 16

wait can you explain how you get the degrees and radiants again i got a little confused on that part