Find, correct to 1 decimal place, the two smallest positive values of θ which staisfy, sin θ °=0.1

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

`sin theta = 0.1`

To solve to `theta` , take the arc sine of 0.1.

`theta = sin^(-1) 0.1`

`theta=5.7391704...`

And if we round it off to one decimal place, the value of `theta` becomes

`theta = 5.7^o`

since the number after .7 is less than 5.

Moreover, sine function is positive not only in Quadrant 1 but also in Quadrant 2. So the other value of theta is:

`theta = 174.3^o`

Since, there is no indicated interval for `theta` , then, we would use the general solution of sine function for all the positive values of `theta` .

Hence, `theta_1 = 5.7 + 360 k` degrees and `theta_2 = 174.3 + 360k` , where k is an integer that is `kgt=0` .

zimiki's profile pic

zimiki | (Level 1) eNoter

Posted on

For very small vallues of θ we can say that sinθ ~= θ

So for θ=0,1 you would get sinθ=0,1

And for the respective vallue in the 2nd Quadrant you could say 

θ' = pi  - θ ~= 3,04

 

- Note that ~= means approximately equal- 

 

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