Question

why there are so many values in sinθ, cosθ, tanθ???
how to find all values???

Answer 1

Kryton, yes there are many values for \(\sin \theta\) , \(\cos \theta\) , \( \tan \theta\) . The answer for your question that why there are so many values for these trigonometric values is that there are many angles. We can put any angle on the place of theta there, and the value will change accordingly.
Like : \(\sin 45 = \cfrac{1}{\sqrt{2}}\) while \(\sin 0 = 0\) . and similarly for cosine and tangent.

Answer 2

@kryton1212 Yo! How's it going?

Answer 3

Can I provide my reasoning here?

Answer 4

yup

Answer 5

\[\rm \sin\theta = \dfrac{opposite}{hypotenuse}\]\[\rm\cos\theta = \dfrac{adjacent}{hypotenuse}\]\[\tan\theta = \rm \dfrac{opposite}{adjacent}\]There are many values for \(\sin\theta,\cos\theta,\tan\theta\) simply because there are many values for \(\rm opposite, adjacent\) and \(\rm hypotenuse\).

Answer 6

so how to find them all

Answer 7

You might understand that opposite, adjacent and hypotenuse are just sides of a right there. Remember that Pythagorean Theorem?\[\rm opposite^2 + adjacent^2 = hypotenuse^2\]Or as they say,\[a^2 + b^2 = c^2\]

Answer 8

yup

Answer 9

So you can use \(a^2 + b^2 =c ^2\) to find the sides of triangles. As it turns out, there are infinitely many right triangles!

Answer 10

There are 2 tricks to memorize them :

i) Practice as many questions of trigonometry that you can do, you will automatically memorize them.

ii) write :0, 1 , 2 , 3 and 4 on a paper.

0 1 2 3 4

divide all of them by 4

0/4 1/4 2/4 3/4 4/4

take square root of all

\(\sqrt{\cfrac{0}{4}}\) , \(\sqrt{\cfrac{1}{4}}\) , \(\sqrt{\cfrac{2}{4}}\) , \(\sqrt{\cfrac{3}{4}}\) , \(\sqrt{\cfrac{4}{4}}\)

we have : 0 , \(\cfrac{1}{2}\) , \(\cfrac{1}{\sqrt{2}}\) , \(\cfrac{\sqrt{3}}{2}\) , 1

these are the values for \(\sin 0 \space , \space \sin 30 \space , \space \sin 45 \space ,\space \sin 60 \space ,\space \sin 90\)

that is : \(\sin 0 = 0\)
\(\sin 30 = \cfrac{1}{2}\)
\(\sin 45 = \cfrac{1}{\sqrt{2}}\)
\(\sin 60 = \cfrac{\sqrt{3}}{2}\)
\(\sin 90 = 1\)

Do the reverse for cos that is write 4,3,2,1,0 and follow the same process

Answer 11

wow

Answer 12

You can find all the values by using your calculator, or by drawing a triangle.

Answer 13

i don't know how to use the ASTC graph

Answer 14

Just remember the definitions and basics.

Answer 15

I presented a trick for your easy kryton. Parth is doing good with explanation for finding them .

Answer 16

You'll learn them no matter what.

Answer 17

^for your ease.

Answer 18

Hmm, there is a way I have memorized the values for basic angles.

Answer 19

You just have to memorize these two triangles... just these two: