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Solution
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Solution provided by AtoZmath.com
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Find the value of other five trigonometric functions if sin(x)=1/2 calculator
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2. Find the value of other five trigonometric functions or solve expression
1. If sin(x)=513 then find other trigonometry
2. If cos(x)=1213 then find other trigonometry
3. If tan(x)=512 then find other trigonometry
4. If csc(x)=135 then find other trigonometry
5. If sec(x)=1312 then find other trigonometry
6. If cot(x)=125 then find other trigonometry
1. If sin(x)=35 then solve cos(x)csc(x)+tan(x)sec(x)
2. If tan(x)=12 then solve 1-tan2(x)1+tan2(x)+2tan(x)1+tan2(x)
3. If sin(x)=45 then solve 1-sin(x)cos(x)+cos(x)1-sin(x)
4. If cos(x)=35 then solve 1-sin(x)cos(x)+cos(x)1-sin(x)
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Example1. If sin(x)=35, find other trigonometry functions sin(x),cos(x),tan(x),csc(x),sec(x),cot(x)Solution:sin(x)=35, in Quadrant-1  Opposite side (y), adjacent side (x) and hypotenuse (r)sin(θ),cos(θ),tan(θ) fromula
sin(θ)=oppositehypotenuse=yr
cos(θ)=adjacenthypotenuse=xr
tan(θ)=oppositeadjacent=yx
csc(θ)=hypotenuseopposite=ry
sec(θ)=hypotenuseadjacent=rx
cot(θ)=adjacentopposite=xy
sin(x)=oppositehypotenuse=yr=35Here y=3 and r=5In triangle ABC, by Pythagoras' theorem r2=x2+y2:.x^2=r^2-y^2=5^2-3^2=25-9=16:.x=sqrt(16)=4 ( :' x is +ve in Quadrant-1) So, x=4,y=3 and r=5(1) sin(x)=y/r=(3)/(5)=3/5(2) cos(x)=x/r=(4)/(5)=4/5(3) tan(x)=y/x=(3)/(4)=3/4(4) csc(x)=r/y=(5)/(3)=5/3(5) sec(x)=r/x=(5)/(4)=5/4(6) cot(x)=x/y=(4)/(3)=4/3
Second Method sin(x)=3/5, in Quadrant-1 (1) cos^2(x)=1-sin^2(x)=1-(3/5)^2=1-9/25=(25-9)/25=16/25:.cos(x)=sqrt(16/25)=4/5=4/5(2) tan(x)=sin(x)/cos(x)=(3/5)/(4/5)=3/5 xx 5/4=3/4=3/4(3) csc(x)=1/sin(x)=1/(3/5)=5/3=5/3(4) sec(x)=1/cos(x)=1/(4/5)=5/4=5/4(5) cot(x)=1/tan(x)=1/(3/4)=4/3=4/3
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Input functions
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Sr No. |
Function |
Input value |
1. |
x^3 |
x^3 |
2. |
sqrt(x) |
sqrt(x) |
3. |
root(3)(x)
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root(3,x)
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4. |
sin(x) |
sin(x) |
5. |
cos(x) |
cos(x) |
6. |
tan(x) |
tan(x) |
7. |
sec(x) |
sec(x) |
8. |
cosec(x) |
csc(x) |
9. |
cot(x) |
cot(x) |
10. |
sin^(-1)(x) |
asin(x) |
11. |
cos^(-1)(x) |
acos(x) |
12. |
tan^(-1)(x) |
atan(x) |
13. |
sin^2(x) |
sin^2(x) |
14. |
log_y(x) |
log(y,x) |
15. |
log_10(x) |
log(x) |
16. |
log_e(x) |
ln(x) |
17. |
e^x |
exp(x) or e^x |
18. |
e^(2x) |
exp(2x) or e^(2x) |
19. |
oo |
inf |
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