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h(x)=3sin(2x-pi)+2

h(x)=3sin⁡(2x−π)+2 h(x)=3 \sin (2 x-\pi)+2

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Full solution

Q. h(x)=3sin⁡(2x−π)+2 h(x)=3 \sin (2 x-\pi)+2
  1. Substitute xx with π4\frac{\pi}{4}: To evaluate the function h(x)h(x) at x=π4x = \frac{\pi}{4}, we need to substitute xx with π4\frac{\pi}{4} in the function h(x)=3sin⁡(2x−π)+2h(x) = 3\sin(2x - \pi) + 2.\newlineCalculation: h(π4)=3sin⁡(2(π4)−π)+2h\left(\frac{\pi}{4}\right) = 3\sin\left(2\left(\frac{\pi}{4}\right) - \pi\right) + 2
  2. Simplify argument of sine function: Simplify the argument of the sine function by multiplying 22 with π/4\pi/4.\newlineCalculation: 2(π/4)=π/22(\pi/4) = \pi/2
  3. Substitute simplified argument: Substitute the simplified argument back into the function.\newlineCalculation: h(π4)=3sin⁡(π2−π)+2h(\frac{\pi}{4}) = 3\sin(\frac{\pi}{2} - \pi) + 2
  4. Simplify argument inside sine function: Simplify the argument inside the sine function by subtracting π\pi from π2\frac{\pi}{2}.\newlineCalculation: π2−π=−π2\frac{\pi}{2} - \pi = -\frac{\pi}{2}
  5. Evaluate sine of simplified argument: Evaluate the sine of the simplified argument.\newlineCalculation: sin⁡(−π2)=−1\sin(-\frac{\pi}{2}) = -1
  6. Multiply result by 33 and add 22: Multiply the result of the sine function by 33 and then add 22 to find the value of h(π4)h(\frac{\pi}{4}).\newlineCalculation: h(π4)=3(−1)+2h(\frac{\pi}{4}) = 3(-1) + 2
  7. Perform multiplication and addition: Perform the multiplication and addition to get the final result.\newlineCalculation: h(π4)=−3+2h(\frac{\pi}{4}) = -3 + 2
  8. Simplify expression: Simplify the expression to find the value of h(π4)h(\frac{\pi}{4}).\newlineCalculation: h(π4)=−1h(\frac{\pi}{4}) = -1

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