maximum and minimum value of a sin x b cos x Trigonometry maxima minima Share Cite edited Jan 10 2020 at 14 32 Blue 76 7k 14 119 234 asked Jan 10 2020 at 12 39 user733666 578 4 13 Use sin x y sinxcosy cosxsiny almagest Jan 10 2020 at 12 46 Add a comment 4 Answers Sorted by 1 By vector calculus
How to find the sinusoidal equation given the maximum and minimum points y A sin b x h k y A cos b x h k A max min 2 P 2 b k max min 2 Example Given the following maximum and minimum points find the sine and cosine equations Max 4 5 Min 2 1 Show Video Lesson Explanation for the correct option We know that the range of a cos b sin is a 2 b 2 a 2 b 2 So the maximum value of a cos x b sin x is a 2 b 2 For example the maximum value of 3 cos 4 sin is given as Now placing a 3 b 4 in a 2 b 2 we get 3 2 4 2 9 16 25 5
maximum and minimum value of a sin x b cos x
maximum and minimum value of a sin x b cos x
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Solved Find The Absolute Maximum And Minimum Values Of The Chegg
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Solved Find The Absolute Maximum And Minimum Values Of F x Chegg
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From here max a sin x b cos x sqrt a 2 b 2 and min a sin x b cos x sqrt a 2 b 2 a sin x cos x frac 1 2 a sin2x and from here max a sin x cos x frac a 2 and min a sin x cos x frac a 2 By considering a right angled triangle with the short sides of length a and b you should be able to see that sin y b a 2 b 2 displaystyle sin y frac b sqrt a 2 b 2 and cos y a a 2 b 2 displaystyle cos y frac a sqrt a 2 b 2
To find the maximum and minimum values just have a look at the equation in its rewritten form The maximum and minimum values are given by k and k respectively So in this case the Tap for more steps f x sin x cos x To find the local maximum and minimum values of the function set the derivative equal to 0 and solve cos x sin x 0 Divide each term in the equation by cos x cos x cos x sin x cos x 0 cos x Cancel the common factor of cos x
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For each function state the amplitude period and midline State the maximum and minimum y values and their corresponding x values on one period for x 0 x 0 State the phase shift and vertical translation if applicable Round answers to two decimal places if Solution For a cosine function the minimum value is 1 and maximum value is 1 1 cos x 2 1 Multiply it by 3 3 3cos x 2 3 Maximum at y 3 and minimum at y 3 To find for what value of x we will have the maximum value and minimum value we should equate Minimum 3cos x 2 3
Mathematics Stack Exchange If y a sinx b cos x C y a sin x b cos x C then find maxima and minima for y y Ask Question Asked 9 years 8 months ago Modified 5 years ago Viewed 3k times 2 I was able to solve it till y a2 b2 sin x C y a 2 b 2 sin x C Examples of several amplitudes of the sine function Combining these figures yields the functions y A B sin x and also y A B cos x These two functions have minimum and maximum values as defined by the following formulas The
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maximum and minimum value of a sin x b cos x - By considering a right angled triangle with the short sides of length a and b you should be able to see that sin y b a 2 b 2 displaystyle sin y frac b sqrt a 2 b 2 and cos y a a 2 b 2 displaystyle cos y frac a sqrt a 2 b 2