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Home > Calculus calculators > For P(3,4), find the value of all six trigonometric functions calculator
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Solution
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Solution provided by AtoZmath.com
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For P(3,4), find the value of all six trigonometric functions calculator
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3. For P(3,4), find the value of all six trigonometric functions
1. For `P(3,4)`, find the value of all six trigonometric functions
2. For `P(15,8)`, find the value of all six trigonometric functions
3. For `P(-8,6)`, find the value of all six trigonometric functions
4. For `P(7,-24)`, find the value of all six trigonometric functions
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Example1. For `P(3,4)`, find value of all six trigonometric functions Solution:`P(3,4)` Opposite side `(y)`, adjacent side `(x)` and hypotenuse `(r)` `sin(theta), cos(theta), tan(theta)` fromula
`sin(theta) = "opposite"/"hypotenuse" = y/r`
`cos(theta) = "adjacent"/"hypotenuse" = x/r`
`tan(theta) = "opposite"/"adjacent" = y/x`
`csc(theta) = "hypotenuse"/"opposite" = r/y`
`sec(theta) = "hypotenuse"/"adjacent" = r/x`
`cot(theta) = "adjacent"/"opposite" = x/y`
Here `x=3` and `y=4` In triangle ABC, by Pythagoras' theorem `r^2 = x^2 + y^2` `=3^2 + 4^2` `=9 + 16` `=25` `:.r=sqrt(25)=5` So, `x=3,y=4 and r=5` `(1)` `sin(theta)=y/r=(4)/(5)=4/5` `(2)` `cos(theta)=x/r=(3)/(5)=3/5` `(3)` `tan(theta)=y/x=(4)/(3)=4/3` `(4)` `csc(theta)=r/y=(5)/(4)=5/4` `(5)` `sec(theta)=r/x=(5)/(3)=5/3` `(6)` `cot(theta)=x/y=(3)/(4)=3/4`
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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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