Let θ be an angle such that tanθ = (6)/(5) and cosθ >...

Let $\theta$ be an angle such that $\tan\theta = \frac{6}{5}$ and $\cos\theta > 0$. Find the exact values of $\sec\theta$ and $\sin\theta$. $\sec\theta = \boxed{} $\sin\theta = \boxed{}$

Transcript

00:01 We are going to do problem number 21 and this question the the expression for sac theta is given sec theta is given that is six by five so we need to find the expression for another technometric functions all technometric functions okay so we will understand that what we can conclude when this information is given so let's say this is the triangle and this is height this is base and this is hypotenous so if sate theta is given this simply means that hypotenius by base is given okay so we have the value of hypotenius we have the value of base so we can easily find the value of height okay by pythagoras theorem pythagoras theorem is hypotenous square equals to base square plus height square so here height is square will be a hypotenous square minus base square so height square will be hypotenous here is six so six is square that is 36 and basis square that is 25 five is 25 now here is square will not be there because we just take it to the right side and put it this under root under root sign so square sign will not be there so from here height is coming out to be 11 under root of 11 so we got the height here now we can easily write we got height also so let me write here we got height also that is under root 11 now you can easily write the value of alternative function so let us start by writing sign theta so this is equals to height by hypotenous so height we got is under root of 11 by hypotaneous we have is 6.

02:09 So let us just find the value of under root 11 and this is divided by this is divided by 6.

02:20 So this is equals to this value is equal to 0 .553.

02:29 Now cossack theta.

02:33 So cossack theta is simply the inverse of sine so this is 1 by sine theta.

02:38 So this will be equals to 1 by 0 .553 so let us just find the value that 1 divide by 0 .553 this is equals to 1 .808 now cost theta cost theta this will be just the opposite of this sec theta okay opposite of sec theta so this will be 5 by 6 so let us just find the value of 5 by 6 so this is 0 .833 now we have 10 theta and cot theta to find so 10 theta so 10 theta is height by base so height here is under root 11 and base here is 5 so let us just find the value under root 11 divide by 5 so this is giving us 0 .6 now cot theta, cot theta is the inverse of 10 theta, that is 1 by 10 theta...

Question

Let $\theta$ be an angle such that $\tan\theta = \frac{6}{5}$ and $\cos\theta > 0$. Find the exact values of $\sec\theta$ and $\sin\theta$. $\sec\theta = \boxed{} $\sin\theta = \boxed{}$

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