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[tex]75 \sin(554 \cos( \tan(31 \sec(2 log(54 ln(64 \times 164) ) ) ) ) ) - 94 + {61}^{13} [/tex]
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[tex]75 \sin(554 \cos( \tan(31 \sec(2 log(54 ln(64 \times 164) ) ) ) ) ) - 94 + {61}^{13} [/tex]
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Answer:
To evaluate the expression 75sin(554cos(tan(31sec(2log(54ln(64×164))))))−94+61/13, let's break it down step by step:
Step 1: Evaluate the innermost functions.
- Calculate ln(64×164):
ln(64×164) = ln(10,496) ≈ 9.25767
- Calculate log(54ln(64×164)):
log(54ln(64×164)) = log(54 * 9.25767) ≈ log(500.48218) ≈ 2.69936
- Calculate sec(2log(54ln(64×164))):
sec(2log(54ln(64×164))) = sec(2 * 2.69936) ≈ sec(5.39872) ≈ -1.00024
- Calculate tan(31sec(2log(54ln(64×164)))):
tan(31sec(2log(54ln(64×164)))) = tan(31 * -1.00024) ≈ tan(-31.00744) ≈ -0.60316
- Calculate cos(tan(31sec(2log(54ln(64×164))))):
cos(tan(31sec(2log(54ln(64×164))))) = cos(-0.60316) ≈ 0.82516
- Calculate sin(554cos(tan(31sec(2log(54ln(64×164)))))):
sin(554cos(tan(31sec(2log(54ln(64×164)))))) = sin(554 * 0.82516) ≈ sin(456.47144) ≈ -0.19303
Step 2: Evaluate the remaining operations.
- Calculate 75sin(554cos(tan(31sec(2log(54ln(64×164)))))):
75sin(554cos(tan(31sec(2log(54ln(64×164)))))) ≈ 75 * -0.19303 ≈ -14.47725
- Calculate 61/13:
61/13 ≈ 4.69231
Step 3: Combine the results.
- Calculate -14.47725 - 94 + 4.69231:
-14.47725 - 94 + 4.69231 ≈ -103.78494
Therefore, the evaluated result of the expression 75sin(554cos(tan(31sec(2log(54ln(64×164))))))−94+61/13 is approximately -103.78494.
Step-by-step explanation:
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