{
"query": {
"display": "$$0+\\cos\\left(2\\right)\\left(0\\right)+e^{-4}$$",
"symbolab_question": "TRIG_EVALUATE#0+\\cos(2)(0)+e^{-4}"
},
"solution": {
"level": "PERFORMED",
"subject": "Trigonometry",
"topic": "Evaluate Functions",
"subTopic": "Simplified",
"default": "\\frac{1}{e^{4}}",
"decimal": "0.01831…",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "$$0+\\cos\\left(2\\right)\\left(0\\right)+e^{-4}=\\frac{1}{e^{4}}$$",
"input": "0+\\cos\\left(2\\right)\\left(0\\right)+e^{-4}",
"steps": [
{
"type": "step",
"result": "=0+\\cos\\left(2\\right)\\cdot\\:0+e^{-4}"
},
{
"type": "interim",
"title": "$$0+\\cos\\left(2\\right)\\cdot\\:0+e^{-4}=\\frac{1}{e^{4}}$$",
"input": "0+\\cos\\left(2\\right)\\cdot\\:0+e^{-4}",
"steps": [
{
"type": "step",
"primary": "Apply rule $$0\\cdot\\:a=0$$",
"result": "=0+0+e^{-4}"
},
{
"type": "interim",
"title": "Simplify",
"input": "0+0+e^{-4}",
"steps": [
{
"type": "step",
"primary": "Apply exponent rule: $$a^{-b}=\\frac{1}{a^b}$$",
"secondary": [
"$$e^{-4}=\\frac{1}{e^{4}}$$"
],
"result": "=0+0+\\frac{1}{e^{4}}",
"meta": {
"practiceLink": "/practice/exponent-practice",
"practiceTopic": "Expand FOIL"
}
},
{
"type": "step",
"primary": "$$0+0=0$$",
"result": "=\\frac{1}{e^{4}}"
}
],
"meta": {
"interimType": "Generic Simplify 0Eq"
}
},
{
"type": "step",
"result": "=\\frac{1}{e^{4}}"
}
],
"meta": {
"solvingClass": "Solver",
"interimType": "Solver"
}
},
{
"type": "step",
"result": "=\\frac{1}{e^{4}}"
}
],
"meta": {
"solvingClass": "Trig Evaluate",
"practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Evaluate%20Functions",
"practiceTopic": "Evaluate Functions"
}
},
"meta": {
"showVerify": true
}
}
Solution
Solution
+1
Decimal
Solution steps
Apply rule
Simplify
Apply exponent rule:
Popular Examples
2+(8cos((pi*3)/3))-(2cos((2pi*3)/3))-arctan(3/2)arcsin((5.93)/(12.02))sin(-(7pi)/6)+cos(-pi/4)arcsin((sqrt(2))/(sqrt(3)))
Frequently Asked Questions (FAQ)
What is the value of 0+cos(2)(0)+e^{-4} ?
The value of 0+cos(2)(0)+e^{-4} is 1/(e^4)