The tax hike of 3.99% will include a 2% rise to pay for adult social care after falls in government funding.
Unions have said the £18m of cuts being made to the budget was putting staff and services under pressure.
The council says the budget is balanced but critics say the plan lacks specific details of where the cuts will fall.
Council leader John Osman said: "As we move forward the financial picture will get worse before it gets better.
"It's not until round about 2020 that the financial status of the council will improve, according to what the government has told us so far."
He added there would be some "quick wins" of cuts which would not affect frontline services.
The opposing Liberal Democrats are calling for more details about which services will be affected.
Leader of the Liberal Democrat County Group Jane Lock said: "It is a disgrace that the Conservatives will not give councillors and residents any information about the cuts coming on 1st April, yet they are happy to increase council tax yet again."
Independent Mike Rigby said: "I'm very worried because it was very clear last year the budget unravelled, so within three months the council admitted it was £24m overspent.
"I'm worried the same thing will happen again this year, particularly this year because we have no detail about where the cuts will fall."

Minister for Crime Prevention James Brokenshire wrote to festival organisers asking them to warn people how such substances could be dangerous.
He also said drug laws would be changed so temporary bans could be introduced on "emerging substances" while scientific advice is sought.
Letters were also sent to councils and police forces in festival areas.
Mr Brokenshire said: "During the festival season we know that people may be tempted to try potentially dangerous new drugs, particularly when they are advertised as 'legal' or 'herbal'.
"That is why we are asking festival organisers and police to work with us to send out the message that these substances may not be safe and could contain illegal drugs.
"We are going to change our drug laws so we can respond quickly to emerging substances by introducing a temporary ban while we seek full scientific advice."
Some drugs previously sold as "legal highs" have now been banned, including mephedrone, now a Class B drug.
The Home Office said that the drug naphyrone is branded as NRG1 and sold as "plant food" or "bath salts", but may contain one or more illegal drugs.
The government said it will not permanently ban a substance without receiving full advice from the Advisory Council on the Misuse of Drugs.
In the letter sent to festival organisers, Mr Brokenshire said: "As part of your preparations for this year's event I ask you to review the measures you have put in place to ensure that your festival is as safe an environment as possible, to help protect the public, especially young people from the potential harms and risks of all drugs."
The government's advice has been welcomed by Melvin Benn, managing director of Festival Republic, which stages the Latitude, Big Chill and Reading and Leeds Festivals.
He said: "I can confirm that we do not allow legal high traders to trade at any Festival Republic festival and fully support the minister's view."

Trustees announced a new partnership deal with Cadw, the Welsh government's historic environment service, resolved "short-term problems that gave rise to concerns over the future" of the museum at Caernarfon.
Last week, trustees said they had not received funding since February.
Culture and Sport Minister John Griffiths said he endorsed the deal.
A statement on the RWF Museum website said the partnership with Cadw will "see the Royal Welch Fusiliers Museum funded to provide visitors to Caernarfon Castle with access to the Welsh government accredited museum and to provide an education service for schools".
The museum, which has been based at Caernarfon Castle since the early 1960s, charts the 300-year history of the RWF, dating back to William III.
The regiment was one of the three Welsh infantry regiments to be merged in 2006 to form The Royal Welsh, though the name lives on as the infantry are known as 1st Battalion The Royal Welsh (The Royal Welch Fusiliers).
Taxpayers in Somerset will face at least a £50 rise in council tax after the Conservative-led county council agreed its budget earlier.
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Organisers of this summer's music festivals have been asked by the government to warn about "legal highs".
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The Royal Welch Fusiliers Museum (RWF) has been saved from closure after its funding was secured.