if sin =-2/5 and tan <0 find the exact value of the other trigonometric functions ?

1 Answer
Shwetank Mauria
Aug 2, 2018

#sinA=-2/5#, #cosA=sqrt21/5#, #tanA=-2/sqrt21#
#cotA=-sqrt21/2#, #secA=5/sqrt21# and #cscA=-5/2#

Explanation:

As #sinA=-2/5# and #tanA < 0# (note that it means #cotA < 0#,

we have #cscA=-5/2# and as #csc^2A=cot^2A+1#

i.e. #cot^2A=csc^2A-1=(-5/2)^2-1=25/4-1=21/4#

and #cotA=-sqrt21/2# (as it is negative) and #tanA=-2/sqrt21#

Hence #cosA=sinA/tanA=(-2/5)/(-2/sqrt21)=sqrt21/5#

and #secA=5/sqrt21#

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