could someone please tell me what the other angle identity of tan is? Thank you much!
"...other angle identity of tan x"?
in relation to which "other" ?
there are many identities dealing with the tangent.
The most important is probably
tan x = sin x/cos x
The Pythagorean Relationship would be
tan^2 x + 1 = sec^2 x
how about tan(2A) = 2tan A/(1-tan^2 A)
yes, i do know those, thank you. but my teacher told us that there is a specific identity for "the other angle". for example, the other angle identity of sinx = cos90-x. I believe the "other angle" identity for tanx is cot90-x but i'm not sure.
yes, you are right, tanx = cot(90-x)
if you are ever unsure about an identity like that pick an obscure angle such as 78.4º and test it with your calculator
tan 78.4 = 4.87162
cot(90-78.4)=cot 11.6º = 1/tan 11.6 = 4.87162
Yes, you are correct! The "other angle" identity for tan x is cot(90 - x). This means that if you take the cotangent of the complementary angle (90 degrees minus x), it will be equal to the tangent of x.
To verify this identity, you can choose an angle, such as 78.4 degrees, and test it using a calculator. Calculate tan 78.4 degrees and cot(90 - 78.4) degrees (which is equivalent to cot 11.6 degrees). If the values match, then the identity is valid. In this case, both calculations yield 4.87162, confirming that tan 78.4 degrees is indeed equal to cot 11.6 degrees.