{
"query": {
"display": "$$\\sin\\left(a\\right)=\\frac{3}{5},\\:\\cos\\left(a\\right)$$",
"symbolab_question": "EQUATION#\\sin(a)=\\frac{3}{5},\\cos(a)"
},
"solution": {
"level": "PERFORMED",
"subject": "Trigonometry",
"topic": "Trig Equations",
"subTopic": "Trig Equations",
"default": "\\mathrm{No\\:Solution\\:for}\\:a\\in\\mathbb{R}",
"meta": {
"showVerify": true
}
},
"steps": {
"type": "interim",
"title": "$$\\sin\\left(a\\right)=\\frac{3}{5},\\:\\cos\\left(a\\right){\\quad:\\quad}$$No Solution for $$a\\in\\mathbb{R}$$",
"input": "\\sin\\left(a\\right)=\\frac{3}{5},\\:\\cos\\left(a\\right)",
"steps": [
{
"type": "interim",
"title": "Apply trig inverse properties",
"input": "\\sin\\left(a\\right)=\\frac{3}{5}",
"result": "a=\\arcsin\\left(\\frac{3}{5}\\right)+2πn,\\:a=π-\\arcsin\\left(\\frac{3}{5}\\right)+2πn",
"steps": [
{
"type": "step",
"primary": "General solutions for $$\\sin\\left(a\\right)=\\frac{3}{5}$$",
"secondary": [
"$$\\sin\\left(x\\right)=a\\quad\\Rightarrow\\quad\\:x=\\arcsin\\left(a\\right)+2πn,\\:\\quad\\:x=π-\\arcsin\\left(a\\right)+2πn$$"
],
"result": "a=\\arcsin\\left(\\frac{3}{5}\\right)+2πn,\\:a=π-\\arcsin\\left(\\frac{3}{5}\\right)+2πn"
}
],
"meta": {
"interimType": "Trig Apply Inverse Props 0Eq"
}
},
{
"type": "step",
"primary": "Solutions for the range $$\\cos\\left(a\\right)$$",
"result": "\\mathrm{No\\:Solution\\:for}\\:a\\in\\mathbb{R}"
}
],
"meta": {
"solvingClass": "Trig Equations",
"practiceLink": "/practice/trigonometry-practice#area=main&subtopic=Trig%20Equations",
"practiceTopic": "Trig Equations"
}
},
"plot_output": {
"meta": {
"plotInfo": {
"variable": "a",
"plotRequest": "\\sin(a)-\\frac{3}{5},\\cos(a)"
},
"showViewLarger": true
}
},
"meta": {
"showVerify": true
}
}
Solution
Solution
Solution steps
Apply trig inverse properties
General solutions for
Solutions for the range
Graph
Popular Examples
Frequently Asked Questions (FAQ)
What is the general solution for sin(a)= 3/5 ,cos(a) ?
The general solution for sin(a)= 3/5 ,cos(a) is No Solution for a\in\mathbb{R}